direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

adaptive control of linear time varying plants abstract in this paper the model reference adaptive control mrac problem of a class of linear time varying ltv plants is considered the plant parameters are assumed to be smooth bounded functions of time which satisfy the usual assumptions of mrac for time invariant plants at each frozen time instant it is first shown that if the plant parameters are sufficiently slowly varying with time a control parameter vector with smooth elements exists such that the closed loop plant behaves almost like a linear time invariant reference model the robust adaptive law proposed in ioannou and tsakalis 1986 ieee trans aut control ac 31 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions it is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

fuzzy adaptive control with state observer for a class of nonlinear discrete time systems with input constraint in this paper an adaptive fuzzy controller is constructed for a class of nonlinear discrete time systems with unknown functions and bounded disturbances the main characteristics of the systems are that they take into account the effect of discrete time dead zone and the system states are not required to be measurable the stability problem of this class of systems is for the first time to be addressed in this paper due to the unavailability of the states and the presence of the discrete time dead zone the controller design becomes more difficult to stabilize the uncertain nonlinear discrete time systems the fuzzy logic systems are used to approximate the unknown functions a fuzzy state observer is designed to estimate the immeasurable states and the effect caused by discrete time dead zone can be solved via establishing an adaptation auxiliary signal based on the lyapunov approach it is proved that all the signals of the closed loop system are the semiglobal uniformly ultimately bounded and the tracking error is made within a small neighborhood around zero the feasibility of the developed control scheme is verified via two simulation examples

a numerically robust state space approach to stable predictive control strategies recent work with predictive control strategies has shown that the stable gpc sgpc approach has significant computational and numerical advantages however sgpc is cast in the transfer function framework which limits its application here we develop a means of extending the results to state space models and show that improved numerical conditioning can be obtained for many stable predictive control strategies

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

on stability of multiobjective nmpc with objective prioritization this paper proposes a new multiobjective model predictive control mo mpc of constrained nonlinear systems according to objective prioritization the mo mpc problem is formulated as a lexicographic optimization problem the optimal solutions are obtained by solving a hierarchy of single objective optimization problems the conditions guaranteeing the recursive feasibility of the optimization problem and stability of the closed loop system are derived which depend only on the most important objective moreover a suboptimal algorithm is presented to reduce the computational demand of mo mpc one characteristic of the proposed mo mpc is that the given objective prioritization is automatically satisfied the theoretical results are illustrated by a comparison study of an example

on tuning leakage for performance robust adaptive control the behavior of a model reference adaptive control mrac system is examined the effect of the inclusion of leakage in the adaptive algorithm is studied and the leakage mechanism of the sigma modification and the e sub 1 modification are discussed a useful approximation is given for a particular mrac problem for the small step size average parameter estimate motion away from an arbitrary stabilizing adaptive controller parameterization arrow diagrams verify the conclusion that designer selected leakage constants must be well chosen in relation to the unknown plant and environment to avoid bursting by an adaptive controller in the absence of adequate excitation by the external forcing function s

discrete time model reference adaptive control of nonlinear dynamical systems using neural networks a multilayer discrete time neural net nn controller is presented for the direct model reference adaptive control of a class of multi input multi output mim0 nonlinear dynamical systems the nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement the nn controller exhibits learning while functioning features instead of learning then control so that control is immediate with no explicit learning phase needed the tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time persistence of excitation pe is not needed linearity in the parameters is not required and certainty equivalence is not used this overcomes several limitations of standard adaptive control the novel weight tuning paradigm for the nn controller is based on the well known delta rule but includes a modification to the learning rate parameter plus a correction term it guarantees tracking as well as bounded nn weights in non i

signatures definitions operators and applications to fuzzy modelling this paper presents a new framework for the symbolic representation of data which is referred to as signatures the definitions of signatures and of signature trees are first given original operators on signatures are next presented i e contraction extension pruning addition multiplication and grafting attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed an example is included to accompany the theoretical results

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

nonlinear adaptive control using neural networks and multiple models in this paper adaptive control of a class of nonlinear discrete time dynamical systems with boundedness of all signals is established by using a linear robust adaptive controller and a neural network based nonlinear adaptive controller and switching between them by a suitably defined switching law the linear controller when used alone assures boundedness of all the signals but not satisfactory performance the nonlinear controller may result in improved response but may also result in instability by using a switching scheme it is demonstrated that improved performance and stability can be simultaneously achieved

stability and boldsymbol l_ 1 gain analysis for positive takagi sugeno fuzzy systems with impulse this paper is concerned with the stability analysis and l 1 gain characterization for positive takagi sugeno fuzzy systems subject to impulse effects the main tool utilized is the construction of an impulse time dependent discretized copositive lyapunov function where the impulse interval partitioning idea is exploited to derive less conservative results for the disturbance free case stability criteria are developed to guarantee global exponential stability of the concerned systems under ranged and constant dwell time constraints the analysis of the influence of the discretizing parameter on the reduction of conservativeness is performed we further employ the proposed impulse time dependent discretized copositive lyapunov function to analyze the l 1 gain performance for the case where external disturbances are considered by performing a grid search for a scalar in an interval all the proposed criteria can be checked via linear programming finally numerical simulations are discussed to illustrate the effectiveness of the theoretical results

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

robust fuzzy control of nonlinear systems using shape adaptive radial basis functions recently various adaptive fuzzy control schemes have been proposed to deal with nonlinear systems whose dynamics are poorly understood by using the parameterized fuzzy approximators however most of the schemes presented so far can only tune the parameters which appear linearly in the parameterized fuzzy approximators the major disadvantage is that the desired approximation error may not be warranted and consequently the control performance could be influenced in this paper we tune not only the linear parameters but also the parameters which appear nonlinearly in the fuzzy approximators to reduce the approximation error and to improve control performance the proposed adaptive controller ensures global stability of the overall adaptive system and achieves desired tracking

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

a general framework to design stabilizing nonlinear model predictive controllers abstract we propose a new model predictive control mpc framework to generate feedback controls for time varying nonlinear systems with input constraints we provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered the supplied sufficient conditions for stability can also be used to analyse the stability of most previous mpc schemes the class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system some important classes of nonlinear systems including some nonholonomic systems can now be stabilized by mpc in addition we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem and thereby reduce the computational effort in the optimization algorithms used to implement mpc

stable fuzzy adaptive control for a class of nonlinear systems abstract in this paper two adaptive fuzzy control schemes for a class of nonlinear systems are proposed each scheme employs a fuzzy control with an adaptive law and a compensation control it is proved that the closed loop system is asymptotically stable based on lyapunov synthesis approach while the identification of the controlled plant is unnecessary finally these schemes are applied to control a chaotic system the simulation results show that our schemes are superior to the scheme of 12

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

fuzzy basis functions comparisons with other basis functions fuzzy basis functions fbf s which have the capability of combining both numerical data and linguistic information are compared with other basis functions because a fbf network is different from other networks in that it is the only one that can combine numerical and linguistic information comparisons are made when only numerical data is available in particular a fbf network is compared with a radial basis function rbf network from the viewpoint of function approximation their architectural interrelationships are discussed additionally a rbf network which is implemented using a regularization technique is compared with a fbf network from the viewpoint of overcoming ill posed problems a fbf network is also compared with specht s probabilistic neural network and his general regression neural network grnn from an architectural point of view a fbf network is also compared with a gaussian sum approximation in which gaussian functions play a central role finally we summarize the architectural relationships between all the networks discussed in this paper

adaptive fuzzy control of a class of siso nonaffine nonlinear systems this paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous time single input single output siso nonaffine nonlinear dynamic systems based on the implicit function theory the existence of an ideal controller that can achieve control objectives is firstly shown since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it a fuzzy system is employed to approximate this unknown ideal control law the adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm this algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law the stability analysis of the closed loop system is performed using a lyapunov approach in particular it is shown that the tracking error converges to a neighborhood of zero the effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system

brief paper improving performance in model predictive control switching cost functionals under average dwell time in this paper we propose a novel switched model predictive control mpc algorithm for nonlinear continuous time systems where we switch between different cost functionals in order to enhance performance thus different performance criteria can be taken into account in order to ensure stability of the resulting closed loop system we consider switching signals which exhibit a certain average dwell time when considering switching signals of this type certain assumptions are common in the switched systems literature in order to ensure stability like a matching condition for the different lyapunov functions and the possibility to find lyapunov functions with an exponential decay rate in this paper we show how these assumptions can be satisfied in the mpc context and thus stability of the proposed switched mpc algorithm can be established

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

stability analysis and systematic design of takagi sugeno fuzzy control systems abstract the stability analysis and systematic design techniques of takagi sugeno t s fuzzy control systems are discussed in this paper in order to make good use of the structural information in rule base to decrease the conservatism of the stability analysis the standard fuzzy partition of the input variables of fuzzy control systems is well defined based on the property analysis of fuzzy control systems with sfp inputs the stability of both the input free t s fuzzy systems and the closed loop t s fuzzy control systems are studied in detail with the extended lyapunov theory and two theorems to check the stability of t s fuzzy control systems are proposed these methods which only require to find a common positive definite symmetric matrix in each maximal overlapped rules group can reduce the conservatism and difficulty of the former stability analysis approaches using the method of parallel distributed compensation a systematic design approach of t s fuzzy control systems is presented the simulation results of three examples show that these methods are effective

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

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

on the stabilizing property of siorhc it is shown that the stabilizing property of siorhc stabilizing i o receding horizon control holds for general stabilizable discrete time linear plants irrespective of the condition that the plant has no poles at the origin

examples when nonlinear model predictive control is nonrobust we consider nominal robustness of model predictive control for discrete time nonlinear systems we show by examples that when the optimization problem involves state constraints or terminal constraints coupled with short optimization horizons the asymptotic stability of the closed loop may have absolutely no robustness that is to say it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and at the same time far from the desired set point this phenomenon does not occur when using model predictive control for linear systems with convex constraint sets we emphasize that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point s in the interior of the feasibility region

multiobjective model predictive control this paper proposes a novel model predictive control mpc scheme based on multiobjective optimization at each sampling time the mpc control action is chosen among the set of pareto optimal solutions based on a time varying state dependent decision criterion compared to standard single objective mpc formulations such a criterion allows one to take into account several often irreconcilable control specifications such as high bandwidth closed loop promptness when the state vector is far away from the equilibrium and low bandwidth good noise rejection properties near the equilibrium after recasting the optimization problem associated with the multiobjective mpc controller as a multiparametric multiobjective linear or quadratic program we show that it is possible to compute each pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular pareto optimal solution furthermore we provide conditions for selecting pareto optimal solutions so that the mpc control loop is asymptotically stable and show the effectiveness of the approach in simulation examples

stability margins of nonlinear receding horizon control via inverse optimality using the nonlinear analog of the fake riccati equation developed for linear systems we derive an inverse optimality result for several receding horizon control schemes this inverse optimality result unifies stability proofs and shows that receding horizon control possesses the stability margins of optimal control laws

finite time stabilization of switched nonlinear systems with partial unstable modes this paper investigates the finite time stabilization problem of switched nonlinear systems sns in the presence of impulse effects where both stable subsystems and unstable subsystems coexist a new notion named mode dependent average switching frequency mdasf is firstly proposed by extending the previous average switching frequency method asf designing mode dependent switching law reveals the tradeoff among stable and unstable modes based on the estimation on transition matrix and gronwall bellman inequality mode dependent feedback controllers are constructed to achieve finite time stability of the closed loop systems finally a numerical example is given to verify the efficiency of the proposed method and the validity of our results

globally stable direct fuzzy model reference adaptive control abstract in the paper a fuzzy adaptive control algorithm is presented it belongs to the class of direct model reference adaptive techniques based on a fuzzy takagi sugeno model of the plant the plant to be controlled is assumed to be nonlinear and predominantly of the first order consequently the resulting adaptive and control laws are very simple and thus interesting for use in practical applications the system remains stable in the presence of unmodelled dynamics disturbances parasitic high order dynamics and reconstruction errors are treated explicitly the global stability of the overall system is proven in the paper i e it is shown that all signals remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high order parasitic dynamics the proposed algorithm is tested on a simulated three tank system its performance is compared to the performance of a classical mrac

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

model predictive control for want of a local control lyapunov function all is not lost we present stability results for unconstrained discrete time nonlinear systems controlled using finite horizon model predictive control mpc algorithms that do not require the terminal cost to be a local control lyapunov function the two key assumptions we make are that the value function is bounded by a k sub spl infin function of a state measure related to the distance of the state to the target set and that this measure is detectable from the stage cost we show that these assumptions are sufficient to guarantee closed loop asymptotic stability that is semiglobal and practical in the horizon length and robust to small perturbations if the assumptions hold with linear or locally linear k sub spl infin functions then the stability will be global or semiglobal for long enough horizon lengths in the global case we give an explicit formula for a sufficiently long horizon length we relate the upper bound assumption to exponential and asymptotic controllability using terminal and stage costs that are controllable to zero with respect to a state measure we can guarantee the required upper bound but we also require that the state measure be detectable from the stage cost to ensure stability while such costs and state measures may not be easy to construct in general we explore a class of systems called homogeneous systems for which it is straightforward to choose them in fact we show for homogeneous systems that the associated k sub spl infin functions are linear thereby guaranteeing global asymptotic stability we discuss two examples found elsewhere in the mpc literature including the discrete time nonholonomic integrator to demonstrate our methods for these systems we give a new result they can be globally asymptotically stabilized by a finite horizon mpc algorithm that has guaranteed robustness we also show that stable linear systems with control constraints can be globally exponentially stabilized using finite horizon mpc without requiring the terminal cost to be a global control lyapunov function

robust model predictive control of stable linear systems a new robust model predictive control mpc algorithm is presented for stable constrained linear plants that is a direct generalization of the nominally stabilizing regulator presented by rawlings and muske model uncertainty is parametrized by a list of possible plants robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant asymptotic stability is demonstrated through a lyapunov argument simulation experiments demonstrate the performance of the algorithm for two example processes

the extremal function associated to intrinsic norms through the study of the degenerate complex monge ampere equation we establish the optimal regularity of the extremal function associated to intrinsic norms of chern levine nirenberg and bedford taylor we prove a conjecture of chern levine nirenberg on the extended intrinsic norms on complex manifolds and verify bedford taylor s representation formula for these norms in general