containment control for partial differential multi agent systems abstract this paper investigates the containment control problem for a class of partial differential multi agent systems which are governed by the parabolic equations heat equations or the second order hyperbolic equations wave equations the distributed containment based feedback control laws are obtained by constructing an appropriate lyapunov functional and under the action of the feedback control laws the containment errors between the followers states and the convex hull spanned by the leaders states on an appropriate sobolev space can converge to zero as time tends to infinity simulation examples are finally used to show the effectiveness of the theoretical analysis

a distributed model predictive control scheme for leader follower multi agent systems abstractin this paper we present a novel receding horizon control scheme for solving the formation problem of leader follower configurations the algorithm is based on set theoretic ideas and is tuned for agents described by linear time invariant lti systems subject to input and state constraints the novelty of the proposed framework relies on the capability to jointly use sequences of one step controllable sets and polyhedral piecewise state space partitions in order to online apply the better control action in a distributed receding horizon fashion moreover we prove that the design of both robust positively invariant sets and one step ahead controllable regions is achieved in a distributed sense simulations and numerical comparisons with respect to centralised and local based strategies are finally performed on a group of mobile robots to demonstrate the effectiveness of the proposed control strategy

neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees in this paper a neuroadaptive control framework for continuous and discrete time nonlinear uncertain dynamical systems with input to state stable internal dynamics is developed the proposed framework is lyapunov based and unlike standard neural network nn controllers guaranteeing ultimate boundedness the framework guarantees partial asymptotic stability of the closed loop system that is asymptotic stability with respect to part of the closed loop system states associated with the system plant states the neuroadaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuously differentiable and that the approximation error of uncertain system nonlinearities lie in a small gain type norm bounded conic sector this allows us to merge robust control synthesis tools with nn adaptive control tools to guarantee system stability finally two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

singular linear systems on lie groups equivalence abstract in this paper we define different kinds of singular systems on lie groups and we analyze some of them furthermore we state sufficient conditions for a general nonlinear singular system defined on a manifold to be equivalent by diffeomorphism to one of these models some examples are computed

disturbance estimator based output feedback exponential stabilization for euler bernoulli beam equation with boundary control in this paper we are concerned with the output feedback exponential stabilization problem for a system plant described by a one dimensional euler bernoulli beam equation the measurements are only the displacement and the angular velocity at the right end an infinite dimensional estimator is designed to estimate the disturbance with the estimated disturbance we propose a state observer that is exponentially convergent to the original system then design two different kinds of stabilizing controllers one is based on the velocity feedback the other is based on the angular velocity feedback in both cases by adopting the riesz basis approach the exponential stability of the closed loop systems is built with guaranteeing that all internal systems are uniformly bounded the numerical experiments are carried out to illustrate the theoretical results

structure properties of min max systems and existence of global cycle time studies min max systems which are dynamic systems including three operations min max with unknown or stochastic parameters some sufficient conditions are given for the existence of global cycle times our results are based on structure properties of min max systems

model predictive control for stochastic resource allocation in this paper we consider a class of stochastic resource allocation problems where resources assigned to a task may fail probabilistically to complete assigned tasks failures to complete a task are observed before new resource allocations are selected the resulting temporal resource allocation problem is a stochastic control problem with a discrete state space and control space that grow in cardinality exponentially with the number of tasks we modify this optimal control problem by expanding the admissible control space and show that the resulting control problem can be solved exactly by efficient algorithms in time that grows nearly linear with the number of tasks the approximate control problem also provides a bound on the achievable performance for the original control problem the approximation is used as part of a model predictive control mpc algorithm to generate resource allocations over time in response to information on task completion status we show in computational experiments that for single resource class problems the resulting mpc algorithm achieves nearly the same performance as the optimal dynamic programming algorithm while reducing computation time by over four orders of magnitude in multiple resource class experiments involving 1000 tasks the model predictive control performance is within 4 of the performance bound obtained by the solution of the expanded control space problem

fuzzy output tracking control of semi linear first order hyperbolic pde systems with matched perturbations abstract this paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi linear first order hyperbolic partial differential equations pdes firstly a t s fuzzy hyperbolic pde model is assumed to be used to accurately represent the semi linear first order hyperbolic pde system subsequently based on the t s fuzzy pde model the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi linear pde system exponentially tracks a desired reference and the state of the system is uniformly bounded in the filippov sense by constructing a strict lyapunov function the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities lmis in space with an equality constraint it has been shown that when these algebraic lmis with an equality constraint are feasible fuzzy tracking control design can be obtained via the existing convex optimization techniques finally the developed design methodology is successfully applied to the control of a semi linear lotka volterra pde system and the achieved results illustrate its effectiveness

application of shifted jacobi pseudospectral method for solving in finite horizon min max optimal control problems with uncertainty abstractthe difficulty of solving the min max optimal control problems m mocps with uncertainty using generalised euler lagrange equations is caused by the combination of split boundary conditions nonlinear differential equations and the manner in which the final time is treated in this investigation the shifted jacobi pseudospectral method sjpm as a numerical technique for solving two point boundary value problems tpbvps in m mocps for several boundary states is proposed at first a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented then by applying the generalised euler lagrange equations and expanding the required approximate solutions as elements of shifted jacobi polynomials finding a solution of tpbvps in nonlinear m mocps with uncertainty is reduced to the solution of a system of algebraic equations moreover the jacobi polynomials are particularly useful for boundary value problems in unbounded

stability preserving maps for finite time convergence super twisting sliding mode algorithm the super twisting algorithm sta has become the prototype of second order sliding mode algorithm it achieves finite time convergence by means of a continuous action without using information about derivatives of the sliding constraint thus chattering associated to traditional sliding mode observers and controllers is reduced the stability and finite time convergence analysis have been jointly addressed from different points of view most of them based on the use of scaling symmetries homogeneity or non smooth lyapunov functions departing from these approaches in this contribution we decouple the stability analysis problem from that of finite time convergence a nonlinear change of coordinates and a time scaling are used in the new coordinates and time space the transformed system is stabilized using any appropriate standard design method conditions under which the combination of the nonlinear coordinates transformation and the time scaling is a stability preserving map are given provided convergence in the transformed space is faster than o 1 t where t is the transformed time convergence of the original system takes place in finite time the method is illustrated by designing a generalized super twisting observer able to cope with a broad class of perturbations

a geometric treatment of implicit differential algebraic equations abstract a differential geometric approach for proving the existence and uniqueness of implicit differential algebraic equations is presented it provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems the differential algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible submanifolds local existence and uniqueness results for differential algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations

information matrices for normal and laplace mixtures the fisher information matrices fims are derived for a mixture of two laplace distributions and a mixture of two normal distributions the expressions for the matrices involve the lerch function practical application of the results is illustrated through two published works on aircraft navigation and borehole geophysics

on homogeneous finite time control for linear evolution equation in hilbert space based on the notion of generalized homogeneity a new algorithm of feedback control design is developed for a plant modeled by a linear evolution equation in a hilbert space with a possibly unbounded operator the designed control law steers any solution of the closed loop system to zero in a finite time a method of homogeneous extension is presented in order to make the developed control design principles to be applicable for evolution systems with nonhomogeneous operators the design scheme is demonstrated for the heat equation with the control input distributed on the segment 0 1

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

sliding mode control of schrodinger equation ode in the presence of unmatched disturbances abstract in this paper we consider boundary stabilization for a cascade of schrodinger equation ode system with both matched and unmatched disturbances the backstepping method is first applied to transform the system into an equivalent target system where the target system is input to state stable to reject the matched disturbance the sliding mode control smc law is designed for the target system the well posedness of the closed loop system is proved and the reachability of the sliding manifold in finite time is justified by infinite dimensional system theory it is shown that the resulting closed loop system is input to state stable a numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed loop system by rejecting the matched disturbance

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

model predictive control based on linear programming the explicit solution we study model predictive control mpc schemes for discrete time linear time invariant systems with constraints on inputs and states that can be formulated using a linear program lp in particular we focus our attention on performance criteria based on a mixed 1 norm namely 1 norm with respect to time and norm with respect to space first we provide a method to compute the terminal weight so that closed loop stability is achieved we then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it the piecewise affine form allows to eliminate online lp as the computation associated with mpc becomes a simple function evaluation besides practical advantages the availability of the explicit structure of the mpc controller provides an insight into the type of control action in different regions of the state space and highlights possible conditions of degeneracies of the lp such as multiple optima

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach

output feedback robust mpc with one free control move for the linear polytopic uncertain system with bounded disturbance in this paper a previous approach for the robust model predictive control mpc for a linear polytopic uncertain system is extended to the case with bounded disturbance and unmeasurable state the controller on line optimizes a free control move followed by an output feedback control law based on the pre specified state estimator a key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem the quadratic boundedness qb of the augmented state is guaranteed by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed controller

sliding mode control of the orr sommerfeld equation cascaded by both the squire equation and ode in the presence of boundary disturbances the sliding mode control smc approach is proposed in this paper for the orr sommerfeld equation cascaded by both the squire equation and ode in which orr sommerfeld and squire equations are su

the active disturbance rejection control to stabilization for multi dimensional wave equation with boundary control matched disturbance in this paper we consider boundary stabilization for a multi dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables the active disturbance rejection control adrc approach is adopted in investigation an extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi dimensional system by infinitely many test functions the disturbance is canceled in the feedback loop together with a collocated stabilizing controller all subsystems in the closed loop are shown to be asymptotically stable in particular the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature the overall picture of the adrc in dealing with the disturbance for multi dimensional partial differential equation is presented through this system the numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction

piecewise affinity of min max mpc with bounded additive uncertainties and a quadratic criterion this brief shows how a min max mpc with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law proofs based on properties of the cost function and the optimization problem are given the boundaries of the regions in which the state space can be partitioned are also treated the results are illustrated by an example

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

adaptive sliding mode control design for a class of uncertain singularly perturbed nonlinear systems this paper addresses adaptive sliding mode control asmc of uncertain singularly perturbed nonlinear uspn systems with guaranteed h control performance first we use takagi sugeno t s fuzzy model to construct the uspn systems then the sliding surface can be determined via linear matrix inequality lmi design procedure second we propose neural network nn based asmc design to stabilise the uspn systems the proposed methods are based on the lyapunov stability theorem the adaptive law can reduce the effect of uncertainty the proposed nn based asmc will stabilise the uspn systems for all 0 simulation result reveals that the proposed nn based asmc scheme has better convergence time compared with the fuzzy control scheme li t h s lin k j 2004 stabilization of singularly perturbed fuzzy systems ieee transactions on fuzzy systems 12 579 595

discontinuous unit feedback control of uncertain infinite dimensional systems control systems driven by a discontinuous unit feedback in a hilbert space are studied the equation which describes a system motion taking place in the discontinuity manifold and further referred to as a sliding mode is derived by means of a special regularization technique based on the sliding mode equation the procedure of synthesis of a discontinuous unit control signal is developed restricted to a class of infinite dimensional systems with finite dimensional unstable part this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed loop system with respect to matched disturbances as an illustration of the capabilities of the procedure proposed a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators

lyapunov approach to output feedback stabilization for the euler bernoulli beam equation with boundary input disturbance we propose a boundary output feedback control law for a one dimensional euler bernoulli beam equation with general external disturbance entering the control end a galerkin approximation scheme is constructed to show the existence of solution to the closed loop system the exponential stability of the closed loop system is obtained by the lyapunov functional method numerical simulations are presented for illustration

time separations of cyclic event rule systems with min max timing constraints the analysis of the time separations of events is a fundamental problem in the design and evaluation of discrete event systems important progresses have been made based on the event rule system model in the last decade the existing results for event rule systems with min and max constraints can be summarized briefly as the exact evaluation of time separations for acyclic systems is np complete for cyclic systems the structural condition of being tightly coupled is sufficient for long term time separations of events to be bounded in this paper we establish a necessary and sufficient structural boundedness condition uniformity for cyclic event rule systems with both min and max constraints tightly coupled systems are shown to be a special class of uniform systems the well known cas algorithm for finding bounds on long term time separations is adapted to find finite bounds for uniform systems our results are obtained by exploring the algebraic structures guiding the evolution of the systems

stabilization of ode with hyperbolic equation actuator subject to boundary control matched disturbance in this paper we consider stabilisation for a cascade of ode and first order hyperbolic equation with external disturbance flowing to the control end the active disturbance rejection control adr

robust dynamic programming for min max model predictive control of constrained uncertain systems we address min max model predictive control mpc for uncertain discrete time systems by a robust dynamic programming approach and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the method uses polyhedral representations of the cost to go functions and feasible sets and performs multiparametric programming by a duality based approach in each recursion step we show how to apply the method to robust mpc and give conditions guaranteeing closed loop stability finally we apply the method to a tutorial example a parking car with uncertain mass

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

tracking control of the uncertain heat and wave equation via power fractional and sliding mode techniques in the present paper preliminary results towards the generalization to the infinite dimensional setting of some well known robust finite dimensional control algorithms are illustrated more specifically we deal with the tracking problem for some classes of linear uncertain infinite dimensional systems evolving in hilbert spaces we design distributed variable structure stabilizers that are shown to be effective in the presence of external disturbances the main focus of the present paper is on the rejection of nonvanishing external disturbances the generalization to the infinite dimensional setting of the well known finite dimensional controllers namely the power fractional controller s p bhat and d s bernstein siam j control optim 38 2000 pp 751 766 and two second order sliding mode control algorithms the twisting and supertwisting algorithms l fridman and a levant higher order sliding modes as a natural phenomenon in control theory in robust control via variable structure and lyapunov techniques springer verlag berlin 1996 pp 107 133 a levant internat j control 58 1993 pp 1247 1263 is the main contribution of the present investigation first the distributed twisting control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation next the finite time state tracking of the unperturbed heat equation is provided by means of a distributed power fractional controller finally the distributed supertwisting controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances constructive proofs of stability are developed via the lyapunov functional technique which leads to simple tuning rules for the controller parameters simulation results are discussed to verify the effectiveness of the proposed schemes

performance output tracking for multidimensional heat equation subject to unmatched disturbance and noncollocated control this paper investigates performance output tracking for a boundary controlled multidimensional heat equation it is assumed that the so called total disturbance which is composed of internal possibly nonlinear uncertainty and external disturbance the equation is subject to is on one part of the boundary and that the control is applied on the rest of the boundary using only partial boundary measurement we first propose an extended state observer to estimate both system state and the total disturbance this allows us to design a servomechanism and then an output feedback controller under the condition that both the reference signal and the disturbance vanish or belong to spaces h 1 0 infty l 1 gamma 1 and l 2 0 infty l 2 gamma 0 respectively we show that the over all control strategy achieves three objectives on the system performance first exponentially output tracking for arbitrary given reference signal second uniformly boundedness of all internal signals and third the internal asymptotic stability of the closed loop system in addition the control strategy turns out to be robust to the measurement noise we provide numerical experiments to illustrate the effectiveness of the proposed control strategy

approximate robust dynamic programming and robustly stable mpc we present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the approximation method uses polyhedral representations of the cost to go function and feasible set and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming bemporad a borrelli f morari m 2003 min max control of constrained uncertain discrete time linear systems ieee transactions on automatic control 48 9 1600 1606 diehl m bjornberg j 2004 robust dynamic programming for min max model predictive control of constrained uncertain systems ieee transactions on automatic control 49 12 2253 2257 we show how to apply the method to robust mpc and give conditions that guarantee closed loop stability we finish by applying the method to a state constrained tutorial example a parking car with uncertain mass

state feedback stabilization and majorizing achievement of min max plus systems the state feedback stabilization of min max plus systems is investigated in this note the concepts of digraph description r s reachability max plus projection direct product etc are introduced to deal with the stability the sufficient condition and the necessary condition for the state feedback stabilization are presented respectively and the desired eigenvalue area is determined moreover the state feedback is constructed for majorizing achievement of the stabilization and the corresponding algorithm is derived

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

maximum likelihood estimation of the multivariate normal mixture model the hessian of the multivariate normal mixture model is derived and estimators of the information matrix are obtained thus enabling consistent estimation of all parameters and their precisions the usefulness of the new theory is illustrated with two examples and some simulation experiments the newly proposed estimators appear to be superior to the existing ones

boundary control of coupled reaction diffusion processes with constant parameters the problem of boundary stabilization is considered for some classes of coupled parabolic linear pdes of the reaction diffusion type with reference to n coupled equations each one equipped with a scalar boundary control input a state feedback law is designed with actuation at only one end of the domain and exponential stability of the closed loop system is proven the treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken the backstepping method is used for controller design and particularly the kernel matrix of the transformation is derived in explicit form of series of bessel like matrix functions by using the method of successive approximations to solve the corresponding pde thus the proposed control laws become available in explicit form additionally the stabilization of an underactuated system of two coupled reaction diffusion processes is tackled under the restriction that only a scalar boundary input is available capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature concentration dynamics of a tubular chemical reactor controlled through a boundary at low fluid superficial velocities when convection terms become negligible

performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance in this paper we consider performance output reference tracking for a wave equation with general harmonic disturbance at one end and the control at the other end we first design a state reference system determined completely by the measured output and the reference signal where the parameter update law is presented an adaptive servomechanism output feedback control is then designed it is shown that the closed loop system is well posed three control objectives are achieved a the performance output is tracking the reference signal b all the internal loops are bounded c when the disturbance and reference are disconnected the closed loop is exponentially stable finally the state of system is shown to be tracking the reference state and the updated parameters are convergent to their true values

constrained min max predictive control modifications of the objective function leading to polynomial complexity in this note an efficient way of implementing a constrained min max predictive controller is presented the new approach modifies the objective function in such a way that the resulting min max problem can be solved in polynomial time different modifications are proposed the main contribution of the note is to provide a robust constrained min max predictive controller that can be implemented in real time the new controller stabilizes the uncertain system

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

a comparison of mean variance efficiency tests abstract we analyse the asymptotic properties of mean variance efficiency tests based on generalised methods of moments and parametric and semiparametric likelihood procedures that assume elliptical innovations we study the trade off between efficiency and robustness and prove that the parametric estimators provide asymptotically valid inferences when the conditional distribution of the innovations is elliptical but possibly misspecified and heteroskedastic we compare the small sample performance of the alternative tests in a monte carlo study and find some discrepancies with their asymptotic properties finally we present an empirical application to us stock returns which rejects the mean variance efficiency of the market portfolio

on impasse points of quasilinear differential algebraic equations abstract this paper presents a mathematical characterization of the impasse points of quasilinear dae s a x g x where then a x is a nxn matrix having constant but not full r n in the domain of interest we show that a reduction procedure permits to reduce the dae to a quasilinear ode al xi xi g1 xi rr and that impasse points correspond to special singularities of the reduced ode impasse points of higher index dae s can also be defined the only difference is that the above reduction procedure takes more than one step

the active disturbance rejection control approach to stabilisation of coupled heat and ode system subject to boundary control matched disturbance we consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation subject to boundary control matched disturbance the active disturbance rejection control approach is applied to estimate in real time the disturbance with both constant high gain and time varying high gain the disturbance is cancelled in the feedback loop the closed loop systems with constant high gain and time varying high gain are shown respectively to be practically stable and asymptotically stable

sliding mode control to stabilization of cascaded heat pde ode systems subject to boundary control matched disturbance in this paper we are concerned with the boundary feedback stabilization of a cascade of heat pde ode system with dirichlet neumann interconnection and with the external disturbance flowing the control end in order to deal with the disturbance the sliding model control smc is integrated with the backstepping approach where the disturbance is supposed to be bounded only the existence and uniqueness of the solution for the closed loop system are proved and the monotonicity of the reaching condition is presented without differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system finally the numerical simulations validate the effectiveness of this method for the system with periodic and normal random disturbances respectively

explicit solution of min max mpc with additive uncertainties and quadratic criterion abstract min max model predictive control mmmpc is one of the strategies proposed to control plants subject to bounded uncertainties this technique is very difficult to implement in real time because of the computation time required recently the piecewise affine nature of this control law has been proved for unconstrained linear systems with quadratic performance criterion however no algorithm to compute the explicit form of the control law was given this paper shows how to obtain this explicit form by means of a constructive algorithm an approximation to mmmpc in the presence of constraints is presented based on this algorithm

generalisation of euler lagrange equations to find min max optimal solution of uncertain systems a major problem in optimal control theory is existing uncertainty in initial state cost function or in state equations in this paper a generalised euler lagrange approach to find min max optimal solution of uncertain systems with uncertain or certain cost function using calculus of variation is considered the work is based on an admissible system path or a trajectory which minimises the maximum value of the functional over all uncertainty first of all a new form of euler lagrange conditions for uncertain systems is presented then several cases are indicated where final condition can be specified or free also necessary conditions are introduced to existence of min max optimal solution of the uncertain systems also the method is generalised when the uncertainties are bounded with using pontryagin s minimum principle finally efficiency of the proposed methods is verified through some examples

analytical expression of explicit mpc solution via lattice piecewise affine function an analytical expression of the explicit solution to linear model predictive control mpc is proposed by the introduction of a lattice piecewise affine pwa function a systematic procedure is developed for building a lattice pwa representation from a continuous explicit mpc solution obtained by a multi parametric program a simple method is presented to remove the redundant parameters in the lattice expression of mpc control laws the effectiveness of this approach is supported by the study of three benchmark mpc problems the proposed analytical expression provides a very efficient and practically viable method for implementing the explicit mpc solutions regarding its online calculation and memory space requirements

on the stability bounds of singularly perturbed systems the stability bound problem of linear time invariant singularly perturbed systems is considered a set of new stability conditions based on the frequency domain representation is derived the stability criteria can be easily verified by computing certain singular values within finite frequency intervals illustrative examples show that the proposed criteria actually induce a less conservative epsilon bound than the existing criteria and for certain cases an infinite epsilon bound may be obtained

active disturbance rejection control for rejecting boundary disturbance from multidimensional kirchhoff plate via boundary control in this paper an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional kirchhoff plate via boundary control the disturbance and control input are assumed to be matched the active disturbance rejection control approach is adopted for developing the algorithm a state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time dependent test functions the proposed control law cancels the disturbance using its estimated value all subsystems in the closed loop are shown to be asymptotically stable simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains

on minimum fisher information distributions with restricted support and fixed variance fisher information is of key importance in estimation theory it also serves in inference problems as well as in the interpretation of many physical processes the mean squared estimation error for the location parameter of a distribution is bounded by the inverse of the fisher information associated with this distribution in this paper we look for minimum fisher information distributions with a restricted support more precisely we study the problem of minimizing the fisher information in the set of distributions with fixed variance defined on a bounded subset s of r or on the positive real line we show that the solutions of the underlying differential equation can be expressed in terms of whittaker functions then in the two considered cases we derive the explicit expressions of the solutions and investigate their behavior we also characterize the behavior of the minimum fisher information as a function of the imposed variance

a dynamic compensator for in domain control of burgers equation this paper addresses the problem of output regulation control of a burgers equation under pointwise in domain actuation a dynamic compensator that generates the in domain control is developed for

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

min max feedback model predictive control for constrained linear systems min max feedback formulations of model predictive control are discussed both in the fixed and variable horizon contexts the control schemes the authors discuss introduce in the control optimization the notion that feedback is present in the receding horizon implementation of the control this leads to improved performance compared to standard model predictive control and resolves the feasibility difficulties that arise with the min max techniques that are documented in the literature the stabilizing properties of the methods are discussed as well as some practical implementation details

the approximation of higher order integrals of the calculus of variations and the lavrentiev phenomenon we prove the following approximation theorem given a function x a b to mathbb r n in the sobolev space bf w nu 1 1 nu geq 1 and epsilon 0 there exists a function x epsilon in bf w nu 1 infty such that begin gather int a b sum i 1 m l i x epsilon nu x epsilon nu 1 psi i t x epsilon x epsilon dotsc x epsilon nu int a b sum i 1 m l i x nu x nu 1 psi i t x x dotsc x nu epsilon begin aligned x epsilon a x a quad x epsilon b x b x epsilon a x a quad x epsilon b x b vdots x epsilon nu a x nu a quad x epsilon nu b x nu b end aligned end gather provided that for every i in 1 dotsc m l i psi i is continuous in a neighborhood of x l i is convex in its second variable and psi i evaluated along x has positive sign we discuss the optimality of our assumptions comparing them with an example of sarychev j dynam control systems 3 1997 pp 565 588 as a consequence we obtain the nonoccurrence of the lavrentiev phenomenon in particular the integral functional int a b l x nu x nu 1 does not exhibit the lavrentiev phenomenon for any given boundary values x a a x b b x a a x b b dotsc x nu a a nu x nu b b nu furthermore we prove the following necessary condition an action functional with lagrangian of the form sum i 1 m l i x nu x nu 1 psi i t x x dotsc x nu with nu geq 0 exhibiting the lavrentiev phenomenon takes the value infty in any neighborhood of a minimizer

unknown input observer design and output feedback stabilization for multi dimensional wave equation with boundary control matched uncertainty abstract in this paper we consider boundary output feedback stabilization for a multi dimensional wave equation with boundary control matched unknown nonlinear internal uncertainty and external disturbance a new unknown input type extended state observer is proposed to recover both state and total disturbance which consists of internal uncertainty and external disturbance a key feature of the proposed observer in this paper is that we do not use the high gain to estimate the disturbance by the active disturbance rejection control adrc strategy the total disturbance is compensated canceled in the feedback loop which together with a collocated stabilizing controller without uncertainty leads to an output feedback stabilizing feedback control it is shown that the resulting closed loop system is well posed and asymptotically stable under weak assumption on internal uncertainty and external disturbance the numerical experiments are carried out to show the effectiveness of the proposed scheme

output feedback robust mpc for lpv system with polytopic model parametric uncertainty and bounded disturbance abstractthe output feedback robust model predictive control mpc for the linear parameter varying lpv system with norm bounded disturbance is addressed where the model parametric matrices are only known to be bounded within a polytope the previous techniques of norm bounding technique quadratic boundedness qb dynamic output feedback and ellipsoid true state bound tsb refreshment formula for guaranteeing recursive feasibility are fused into the newly proposed approaches in the notion of qb the full lyapunov matrix is applied for the first time in this context the single step dynamic output feedback robust mpc where the infinite horizon control moves are parameterised as a dynamic output feedback law is the main topic of this paper while the multi step method is also suggested in order to strictly guarantee the physical constraints the outer bound of the true state replaces the true state itself so tightness of this bound has a major effect on the control performance in order to ti

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

optimal companding vector quantization for circularly symmetric sources in this paper it is shown that optimal z 2 lattice vector quantization can be implemented using radial companding technique we derive the optimal vector compressor function for radial compander of memoryless gaussian source this result is obtained by taking into consideration the source geometry and by establishing the relation between the volumes and the point densities at the compressor input and compressor output we also derive the linearized model the piecewise linear compander its performance closely approaches that of optimal vector quantization for example for r 8bits dimension and l 16 regions the difference between corresponding distortions is about 0 037db while the asymptotic performances are identical

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

a search algorithm for a class of optimal finite precision controller realization problems with saddle points with game theory we review the optimal digital controller realization problems that maximize a finite word length fwl closed loop stability measure for a large class of these optimal fwl controller realization problems which have saddle points a minimax based search algorithm is derived for finding a global optimal solution the algorithm consists of two stages in the first stage the closed form of a transformation set is constructed which contains global optimal solutions in the second stage a subgradient approach searches this transformation set to obtain a global optimal solution this algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these fwl realization problems furthermore for a small class of optimal fwl controller realization problems which have no saddle point the proposed algorithm also provides useful information to help solve them

ultimate periodicity of orbits for min max systems the ultimate periodicity theorem is an important result in min max systems theory it was first proved by olsder and perennes in their unpublished work in this paper we present a new proof this proof is also based on two important theorems the existence of cycle time for any min max function and the nussbaum sine theorem however two different techniques pure min max function and conditional redundancy are used to obtain two important intermediate results the purpose of this paper is to provide a simple alternate proof to the ultimate periodicity theorem

almost riemannian geometry on lie groups a simple almost riemannian structure ars on a lie group g is defined by a linear vector field that is an infinitesimal automorphism and dim g 1 left invariant ones we state results about the singular locus the abnormal extremals and the desingularization of such arss and these results are illustrated by examples on the two dimensional affine and the heisenberg groups these arss are extended in two ways to homogeneous spaces and a necessary and sufficient condition for an ars on a manifold to be equivalent to a general ars on a homogeneous space is stated

finite time stability and robust control synthesis of uncertain switched systems stability analysis is developed for uncertain nonlinear switched systems while being asymptotically stable and homogeneous of degree q 0 these systems are shown to approach the equilibrium point in finite time restricted to second order systems this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations based on this fundamental property switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m vector relative degree 2 2 t the controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts the proposed synthesis procedure is illustrated via application to a friction servo motor

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

boundary time varying feedbacks for fixed time stabilization of constant parameter reaction diffusion systems in this paper the problem of fixed time stabilization of constant parameter reaction diffusion partial differential equations by means of continuous boundary time varying feedbacks is considered moreover the time of convergence can be prescribed in the design the design of time varying feedbacks is carried out based on the backstepping approach using a suitable target system with a time varying coefficient one can state that the resulting kernel of the backstepping transformation is time varying and rendering the control feedback to be time varying as well explicit representations of the kernel solution in terms of generalized laguerre polynomials and modified bessel functions are derived the fixed time stability property is then proved a simulation example is presented to illustrate the main results

disturbance estimator and servomechanism based performance output tracking for a 1 d euler bernoulli beam equation in this paper we consider performance output tracking for a one dimensional euler bernoulli beam equation with boundary moment control and unmatched internal uncertainty and external disturbance for such system the reference feng and guo 2017 firstly studied the active disturbance rejection control adrc problem we design an infinite dimensional disturbance estimator to estimate the total disturbance internal uncertainty and external disturbance and the system state simultaneously a servomechanism generated by the reference signal is designed based on the estimated total disturbance we design an output feedback control law such that the performance output signal tracks the reference signal and all the signals of closed loop system are bounded some illustrative simulations are presented

the explicit constrained min max model predictive control of a discrete time linear system with uncertain disturbances in this technical brief we develop an algorithm to determine the explicit solution of the constrained min max model predictive control problem for a discrete time linear system with bounded additive uncertain disturbance the control law is determined to be piecewise affine from a quadratic cost function and the state space is partitioned into corresponding polyhedral cones by moving the on line implementation to an off line explicit evaluation the computational burden is decreased and the applicability of min max optimization is broadened the results of this approach are shown via computer simulations