technical communique differential geometric condition for feedback complete linearization of stochastic nonlinear system necessary and sufficient condition is obtained for the feedback complete linearization problem for stochastic nonlinear systems

on constructing constrained control lyapunov functions for linear systems this works considers the problem of control of linear systems with input constraints the notion of control lyapunov functions clfs is first generalized and relaxed to define a constrained control lyapunov function cclf and a constructive procedure for cclf is subsequently presented

a framework for robustness analysis of constrained finite receding horizon control a framework for robustness analysis of input constrained finite receding horizon control is presented under the assumption of quadratic upper bounds on the finite horizon costs we derive sufficient conditions for robust stability of the standard discrete time linear quadratic receding horizon control formulation this is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms lending itself to s procedure tools which are used to convert robustness questions to tractable convex conditions robustness with respect to plant model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities simple examples demonstrate the approach

dimensionality of biinfinite systems abstract the problem of determining the uniqueness of the coefficient of interpolation of m compactly supported real functions with a biinfinite sequence of interpolation points leads to the study of the kernel z of the biinfinite block toeplitz matrix d a b a b the dimension of z is found by considering the maximal solvable subspace v relative to a and b further results are obtained using the kronecker canonical form of the matrix pencil a b and restricted generalized inverses of a and b

global predictive regulation of null controllable input saturated linear systems a predictive regulator is described for stabilizing linear plants subject to polyhedral input constraints while the asymptotic stability of general linear plants is ensured subject to a set membership condition on the initial state global asymptotic and semiglobal exponential regulation is achieved for input saturated plants which are asymptotically null controllable with bounded inputs the design knobs of the regulator can be chosen off line so as to compromise between nonconservative regulation performance and computational complexity and an online optimization problem of prequantifiable numerical burden results

state space approach to nonlinear predictive generalised minimum variance control a nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete time multivariable systems the plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open loop unstable and is represented in state space model form the multi step predictive control cost index to be minimised involves both weighted error and control signal costing terms the solution for the control law is derived in the time domain using a general operator representation of the process the controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear in the asymptotic case where the plant is linear the controller reduces to a state space version of the well known gpc controller

nonlinear stochastic receding horizon control stability robustness and monte carlo methods for control approximation this work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately a number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors in each case it is shown that the controller approximation errors do not accumulate even over an infinite time frame and the process converges exponentially fast to a small neighbourhood of the origin in addition to this analysis an approximation method for receding horizon optimal control is proposed based on monte carlo simulation this method is derived via the feynman kac formula which gives a stochastic interpretation for the solution of a hamilton jacobi bellman equation associated with the true optimal controller it is shown and it is a prime motivation for this study that this particular controller approximation method practically stabilises the underlying nonlinear process

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

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

generalized receding horizon control of fuzzy systems based on numerical optimization algorithm the optimal control of fuzzy systems with constraints is still an open problem our focus concerns the optimal control problem of fuzzy systems derived from receding horizon control rhc schemes we consider methods to numerically compute the value function for general fuzzy systems the numerical method that is developed using the finite difference with sigmoidal transformation is a stable and convergent algorithm for the hamilton jacobi bellman hjb equation an optimization procedure is developed to increase the calculation accuracy with less computation time a parallel processing method is employed in the optimization procedure the optimization results are applied to the controller design of general fuzzy dynamic systems employing the principle of conventional rhc schemes rhc form controllers are designed for some classes of fuzzy dynamic systems the basic ideas are as follows first the value function is calculated by numerical methods then the value function is used as controller design parameters to redesign rhc controllers for fuzzy systems which is motivated by the inverse lyapunov function design method it is proven that the closed loop system is asymptotically stable an engineering implementation of the controller redesign scheme is discussed meanwhile the parallel processing framework that can improve the closed loop performance is also introduced

brief a receding horizon approach to the nonlinear h control problem the receding horizon rh methodology is extended to the design of a robust controller of h type for nonlinear systems using the nonlinear analogue of the fake h algebraic riccati equation we derive an inverse optimality result for the rh schemes for which increasing the horizon causes a decrease of the optimal cost function this inverse optimality result shows that the input output map of the closed loop system obtained with the rh control law has a bounded l 2 gain robustness properties of the nonlinear h control law in face of dynamic input uncertainty are considered

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

model predictive control of continuous time nonlinear systems with piecewise constant control a new model predictive control mpc algorithm for nonlinear systems is presented the plant under control the state and control constraints and the performance index to be minimized are described in continuous time while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times in so doing the optimization is performed with respect to sequences as in discrete time nonlinear mpc but the continuous time evolution of the system is considered as in continuous time nonlinear mpc

the equivalence between infinite horizon optimal control of stochastic systems with exponential of integral performance index and stochastic differential games a new method based on the theory of large deviations from the invariant measure is introduced for the analysis of stochastic systems with an infinite horizon exponential of integral performance index it is shown that the infinite horizon optimal exponential of integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system as an application of the developed technique the infinite horizon risk sensitive lqg problem is analyzed for both the completely observed and partially observed case

generalized terminal state constraint for model predictive control a terminal state equality constraint for model predictive control mpc laws is investigated where the terminal state input pair is not fixed a priori but it is a free variable in the optimization the approach named generalized terminal state constraint can be used for both tracking mpc i e when the objective is to track a given steady state and economic mpc i e when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state it is shown that the proposed technique provides in general a larger feasibility set with respect to the existing approaches given the same prediction horizon moreover a new receding horizon strategy is introduced exploiting the generalized terminal state constraint under mild assumptions the new strategy is guaranteed to converge in finite time with arbitrarily good accuracy to an mpc law with an optimally chosen terminal state constraint while still enjoying a larger feasibility set the features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts

lyapunov based model predictive control of stochastic nonlinear systems in this work we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty the lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained the key idea is to use stochastic lyapunov based feedback controllers with well characterized stabilization in probability to design constraints in the lmpc that allow the inheritance of the stability properties by the lmpc the application of the proposed lmpc method is illustrated using a nonlinear chemical process system example

stabilization of nonlinear systems with state and control constraints using lyapunov based predictive control this work considers the problem of stabilization of nonlinear systems subject to state and control constraints for cases where the state constraints need to be enforced at all times hard constraints and where they can be relaxed for some time soft constraints we propose a lyapunov based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions an auxiliary lyapunov based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation for the case when the state constraints are soft we propose a switched predictive control strategy that reduces the time during which state constraints are violated driving the states into the state and input constraints feasibility region of the lyapunov based predictive controller we demonstrate the application of the lyapunov based predictive controller designs through a chemical process example

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

the geometry of blueprints part i algebraic background and scheme theory abstract in this paper we introduce the category of blueprints which is a category of algebraic objects that include both commutative semi rings and commutative monoids this generalization allows a simultaneous treatment of ideals resp congruences for rings and monoids and leads to a common scheme theory in particular it bridges the gap between usual schemes and f 1 schemes after kato deitmar and connes consani beside this unification the category of blueprints contains new interesting objects as improved cyclotomic field extensions f 1 n of f 1 and archimedean valuation rings it also yields a notion of semiring schemes this first paper lays the foundation for subsequent projects which are devoted to the following problems tits idea of chevalley groups over f 1 congruence schemes sheaf cohomology k theory and a unified view on analytic geometry over f 1 adic spaces after huber analytic spaces after berkovich and tropical geometry

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

intervalwise receding horizon h sub spl infin tracking control for discrete linear periodic systems in this paper a fixed horizon h sub spl infin tracking control htc for discrete time varying systems is obtained in a state feedback form from the htc an intervalwise receding horizon htc ihtc is suggested for discrete periodic systems conditions are proposed under which ihtc can stabilize a closed loop system it is shown that under these conditions ihtc guarantees an h sub spl infin norm bound and that ihtc with integral action provides zero offset for a constant command signal the performance of ihtc is compared with those of existing controls via an example the results in this paper are also applicable to time invariant systems which belong to the class of periodic systems

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

constrained infinite horizon linear quadratic regulation of discrete time systems we are concerned with the output norm constrained infinite horizon linear quadratic regulation problem where the underlying state control constraints are specified by curved rather than polyhedral surfaces each suboptimal problem admits an exact convex synthesis condition expressed by an increasing union of linear matrix inequalities and results in an eventually time invariant controller satisfying the desired performance level subject to given constraints and closed loop stability the output norm constrained minimum time control problem is also dealt with as a corollary

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

on the trade off between feasibility and performance in bilinear and state affine model based predictive control closed loop stabilizing model based predictive control mpc algorithms for discrete time bilinear and state affine models are presented stability of the closed loop is obtained through the use of an appropriate end point weighting and end point inequality constraint in this way the infinite horizon performance index is bounded from above by the objective function that is minimized in the mpc algorithm this paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off line the region that is defined by the end point inequality constraint in order to improve the performance of the mpc algorithm the conservatism of the upper bound on the infinite horizon performance index is reduced in the on line computations

stein domains in banach algebraic geometry abstract in this article we give a homological characterization of the topology of stein spaces over any valued base field in particular when working over the field of complex numbers we obtain a characterization of the usual euclidean transcendental topology of complex analytic spaces for non archimedean base fields the topology we characterize coincides with the topology of the berkovich analytic space associated to a non archimedean stein algebra because the characterization we used is borrowed from a definition in derived geometry this work should be read as a derived perspective on analytic geometry

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

analytic geometry over f1 and the fargues fontaine curve abstract this paper develops a theory of analytic geometry over the field with one element the approach used is the analytic counter part of the toen vaquie theory of schemes over f 1 i e the base category relative to which we work out our theory is the category of sets endowed with norms or families of norms base change functors to analytic spaces over banach rings are studied and the basic spaces of analytic geometry e g polydisks are recovered as a base change of analytic spaces over f 1 we conclude by discussing some applications of our theory to the theory of the fargues fontaine curve and to the ring of witt vectors

existence and computation of infinite horizon model predictive control with active steady state input constraints this note addresses the existence and implementation of the infinite horizon controller for the case of active steady state input constraints this case is important because in many practical applications controllers are required to operate at the boundary of the feasible region for instance in order to maximize global economic objectives for this case the usual finite horizon parameterizations with terminal cost cannot be applied and optimal solutions are not generally available we propose here an iterative algorithm that generates two finite horizon approximations to the true infinite horizon problem where the solution to one of the approximations yields an upper bound on the true optimum while the other approximation yields a lower bound we show convergence of both bounding approximations to the optimal solution as the horizon length in the approximations is increased we outline a procedure based on this result to provide a solution to the infinite horizon problem that is exact to within any user specified tolerance finally we present an example that includes a comparison between optimal and suboptimal controllers

a linear programming approach to constrained robust predictive control a receding horizon predictive control algorithm for systems with model uncertainty and input constraints is developed the proposed algorithm adopts the receding horizon dual mode i e free control moves and invariant set paradigm the approach is novel in that it provides a convenient way of combining predictions of control moves which are optimal in the sense of worst case performance with large target invariant sets thus the proposed algorithm has a large stabilizable set of states corresponding to a cautious state feedback law while enjoying the good performance of a tightly tuned but robust control law unlike earlier approaches which are based on qp or semidefinite programming here computational complexity is reduced through the use of lp

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

output feedback lyapunov based predictive control of stochastic nonlinear systems this paper considers the problem of output feedback control of stochastic nonlinear systems a predictive controller is designed for which stability and feasibility in a probabilistic sense are guaranteed from an explicitly characterized region of attraction the controller s performance is characterized by its risk of allowing destabilizing system behavior since the controller design relies on certain convergence properties of the state observer a compatible stochastic high gain type observer design is also presented finally simulation results illustrating the efficacy of the design are presented

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

tracking control of nonlinear systems with bounded controls and control rates abstract the problem of tracking control of a class of nonlinear systems subject to control and control rate constraints is considered a continuous time predictive control approach is used to derive the nonlinear constrained control law asymptotically stable tracking is ensured in the absence of saturation the control and control rate constraints are guaranteed to be strictly satisfied by the control law an example is given to demonstrate the effectiveness of the method

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

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

a factorization theorem for banded matrices in this paper we prove a factorization theorem for strictly m banded totally positive matrices we show that such a matrix is a product of m one banded matrices with positive entries a bi infinite matrix a ai i ca i and ai i n ai i o these matrices arise quite freqiently in applications and recently the have been the subject of several independent investigations 2 3 in this paper we prove a factorization theorem for strictly m handed totally positive matrices we show that such a matrix is a product of m one banded matrices with positive entries let us begin by recalling that a matrix a is totally positive if and only if ull its minors are nonnegative

nominally robust model predictive control with state constraints in this paper we present robust stability results for constrained discrete time nonlinear systems using a finite horizon model predictive control mpc algorithm for which we do not require the terminal cost to have any particular properties we introduce a definition that attempts to characterize the robustness properties of the mpc optimization problem we assume the systems under consideration satisfy this definition for which we give sufficient conditions and make two further assumptions these are that the value function is bounded by a kinfin function of a state measure related to the distance from the state to some target set and that this measure is detectable from the stage cost used in the mpc algorithm we show that these assumptions lead to stability that is robust to sufficiently small disturbances while in general the results are semiglobal and practical when the detectability and upper bound assumptions are satisfied with linear kinfin functions the stability and robustness are either semiglobal or global with respect to the feasible set we discuss algorithms employing terminal inequality constraints and also provide a specific example of an algorithm that employs a terminal equality constraint

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

receding horizon control of nonlinear systems without differentiability of the optimal value function abstract in this paper we show that receding horizon control when applied to a class of nonlinear systems has stabilizing properties our assumptions are necessarily fairly strong because they guarantee implicity that a smooth stabilizing feedback can be constructed this is an extension of our previous results which require the finite horizon value function to be continuously differentiable and therefore applies to a more restricted class of system continuous differentiability of the value function is replaced by local lipschitz continuity dini derivatives and a generalization of the invariance principle are employed to establish stability

homotopical algebraic geometry i topos theory this is the rst of a series of papers devoted to lay the foundations of algebraic geometry in homotopical and higher categorical contexts in this rst part we investigate a notion of higher topos for this we use s categories i e simplicially enriched categories as models for certain kind of 1 categories and we develop the notions of s topologies s sites and stacks over them we prove in particular that for an s category t endowed with an s topology there exists a model category of stacks over t generalizing the model category structure on simplicial presheaves over a grothendieck site of a joyal and r jardine we also prove some analogs of the relations between topologies and localizing subcategories of the categories of presheaves by proving that there exists a one to one correspodence between s topologies on an s category t and certain left exact bouseld localizations of the model category of pre stacks on t based on the above results we study the notion of model topos introduced by c rezk and we relate it to our model categories of stacks over s sites in the second part of the paper we present a parallel theory where s categories s topologies and s sites are replaced by model categories model topologies and model sites we prove that a canonical way to pass from the theory of stacks over model sites to the theory of stacks over s sites is provided by the simplicial localization construction of dwyer and kan as an example of application we propose a denition of etale k theory of ring spectra extending the etale k theory of commutative rings