controllability and stabilizability of a class of continuous piecewise affine dynamical systems this paper studies controllability and stabilizability of continuous piecewise affine dynamical systems which can be considered as a collection of ordinary finite dimensional linear input state output systems together with a partition of the product of the state space and input space into full dimensional polyhedral regions each of these regions is associated with one particular linear system from the collection the main results of the paper are popov belevitch hautus type necessary and sufficient conditions for both controllability and stabilizability of such systems

optimization of lyapunov invariants in verification of software systems the paper proposes a control theoretic framework for verification of numerical software systems and puts forward software verification as an important application of control and systems theory the idea is to transfer lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications these include but are not limited to absence of overflow absence of division by zero termination in finite time absence of dead code and certain user specified assertions central to this framework are lyapunov invariants these are properly constructed functions of the program variables and satisfy certain properties analogous to those of lyapunov functions along the execution trace the search for the invariants can be formulated as a convex optimization problem if the associated optimization problem is feasible the result is a certificate for the specification

a clustering technique for the identification of piecewise affine systems we propose a new technique for the identification of discrete time hybrid systems in the piecewise affine pwa form this problem can be formulated as the reconstruction of a possibly discontinuous pwa map with a multi dimensional domain in order to achieve our goal we provide an algorithm that exploits the combined use of clustering linear identification and pattern recognition techniques this allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures moreover the clustering step used for classifying the datapoints is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure

hybrid model predictive control application towards optimal semi active suspension the optimal control problem of a quarter car semi active suspension has been studied in the past considering that a quarter car semi active suspension can either be modelled as a linear system with state dependent constraint on control of actuator force input or a bi linear system with a control of variable damping coefficient saturation the seemingly simple problem poses several interesting questions and challenges does the saturated version of the optimal control law derived from the corresponding un constrained system i e clipped optimal remain optimal for the constrained case as suggested in some previous publications or should the optimal deviate from the clipped optimal as suggested in other publications if the optimal control law of the constrained system does deviate from its unconstrained counter part how different are they what is the structure of the optimal control law does it retain the linear state feedback form as the unconstrained case in this paper we attempt to an

on the necessity of the invariance conditions for reach control on polytopes abstract we study the reach control problem rcp to make the solutions of an affine system defined on a polytopic state space reach and exit a prescribed facet of the polytope in finite time without first leaving the polytope so called invariance conditions are used to prevent solutions from leaving the polytope through facets which are not designated as the exit facet these conditions are known to be necessary for solvability of the rcp on polytopes by continuous state feedback we study whether the invariance conditions are also necessary for solvability of the rcp on polytopes by open loop controls we show by way of a counterexample that surprisingly the answer is negative we identify a suitable class of polytopes for which the invariance conditions remain necessary conditions

efficient online solution of multi parametric mixed integer quadratic problems this paper considers model predictive control of a class of piecewise affine systems and introduces a method to reduce the complexity of the optimisation problem which is solved online the optimisation problem is a mixed integer quadratic program which is parameterised by the initial state of the system dynamics the complexity of the problem solved online is reduced by moving part of the computational burden offline in the offline computations the structure of the mixed integer problem is explored to determine a polytopic partition of the set of initial states each polytope of the partition is then considered and it is determined which integer combinations can cannot be optimal given that the initial state is contained in the current polytope the result of the offline computations is that each polytope is associated with the set of potentially optimal integer combinations the online solution of the mixed integer problem consists of a two step procedure first it is determined which polytope conta

equivalent piecewise affine models of linear hybrid automata in this technical note we examine the relationship between linear hybrid automata lha and piecewise affine pwa systems while a lha is an autonomous non deterministic model a pwa is a deterministic model with inputs through the key idea of modeling the uncertainty associated with lha transitions as input disturbances in a pwa model by extending continuous time pwa models to include the dynamics of discrete states and resets we show in a constructive way that a lha can be equivalently represented as a pwa system where equivalent means that the two systems generate the same trajectories besides filling in a missing theoretical link between the lha modelling framework and the pwa modelling framework the result has the practical advantage of enabling the use of several existing control theoretical tools developed for pwa models to a wider class of hybrid systems

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

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

improved algorithm for mixed integer quadratic programs and a computational study in a recent paper 6 we suggested an algorithm for solving complicated mixed integer quadratic programs based on an equivalent formulation that employs a nonsingular transformation of variables the objectives of the present paper are two first to present an improved version of this algorithm which reduces substantially its computational requirements second to report on the results of a computational study with the revised algorithm

improved error bounds for freezing solutions of linear boundary value problems for the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by shahruz and schwartz appl math comput 60 1994 285 comput math appl 28 1994 75 a different freezing technique global freezing is also proposed it is shown that this new technique is easy to implement for numerical computation of the solutions moreover the corresponding solution has an error bound similar to that of the freezing method

model predictive control for uncertain max min plus scaling systems in this paper we extend the classical min max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization minimization addition and scalar multiplication and that we call max min plus scaling mmps systems provided that the stage cost is an mmps expression and considering only linear input constraints then the open loop min max model predictive control problem for mmps systems can be transformed into a sequence of linear programming problems hence the min max model predictive control problem for mmps systems can be solved efficiently despite the fact that the system is non linear a min max feedback model predictive control approach using disturbance feedback policies is also presented which leads to improved performance compared to the open loop approach

iterative learning control for non linear systems described by a blended multiple model representation this paper deals with the design of gain scheduling based iterative learning controllers for continuous time non linear systems described by a blended multiple model representation sufficient conditions guaranteeing the convergence of the infinity norm as well as the u norm of the tracking error are derived the effectiveness of the proposed control scheme is illustrated on an example of a non affine in input system

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

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

cardinality constrained linear quadratic optimal control as control implementation often incurs not only a variable cost associated with the magnitude or energy of the control but also a setup cost we consider a discrete time linear quadratic lq optimal control problem with a limited number of control implementations termed in this technical note the cardinality constrained linear quadratic optimal control cclq we first derive a semi analytical feedback policy for cclq problems using dynamic programming dp due to the exponential growth of the complexity in calculating the action regions however dp procedure is only efficient for cclq problems with a scalar state space recognizing this fact we develop then two lower bounding schemes and integrate them into a branch and bound bnb solution framework to offer an efficient algorithm in solving general cclq problems adopting the devised solution algorithm for cclq problems we can solve efficiently the linear quadratic optimal control problem with setup costs

a control problem for affine dynamical systems on a full dimensional polytope given an affine system on a full dimensional polytope the problem of reaching a particular facet of the polytope using continuous piecewise affine state feedback is studied necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope special attention is paid to affine systems on full dimensional simplices in this case the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law that solves the reachability problem under consideration

enumeration based approach to solving parametric linear complementarity problems this paper presents a solution method for parametric linear complementarity problems plcp that relies on an enumeration technique to discover all feasible bases the enumeration procedure is based on evaluating all possible combinations of active constraints and testing for feasibility although the enumeration approach is known to grow exponentially in the number of constraints the formulation of the plcp allows incorporation of cheap rank tests to quickly prune the infeasible directions in the exploration the motivation for the development of the enumeration based plcp solver is that it represents a direct method to solve parametric linear and quadratic optimization problems as well as their mixed integer counterparts these types of problems often arise in the field of model predictive control for linear and hybrid systems the enumeration based plcp solver offers another alternative to compute explicit solutions in the field of hybrid model predictive control that can be extremely effective in some important cases

the lempel ziv algorithm and message complexity data compression has been suggested as a nonparametric way of discriminating between message sources compressions obtained from a lempel ziv algorithm for relatively short messages such as those encountered in practice are examined the intuitive notion of message complexity has less connection with compression than one might expect from known asymptotic results about infinite messages nevertheless discrimination by compression remains an interesting possibility

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

brief paper tracking and synchronisation for a class of pwa systems in this paper the tracking problem for a class of discontinuous piecewise affine pwa systems is addressed we propose an observer based output feedback control design consisting of a feedforward a piecewise affine feedback law and a model based observer solving the tracking problem these synthesis results can also be employed to tackle the master slave synchronisation problem for pwa systems it is shown that for certain classes of pwa systems the design is characterised in terms of linear matrix inequalities the results are illustrated by application to mechanical systems with discontinuous friction characteristics

stabilizing polynomial approximation of explicit mpc a given explicit piecewise affine representation of an mpc feedback law is approximated by a single polynomial computed using linear programming this polynomial state feedback control law guarantees closed loop stability and constraint satisfaction the polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage

impulsive and hybrid dynamical systems stability dissipativity and control s book review w m haddad v s chellaboina and s g nersesov

optimistic optimization for model predictive control of max plus linear systems model predictive control for max plus linear discrete event systems usually leads to a nonsmooth nonconvex optimization problem with real valued variables which may be hard to solve efficiently an alternative approach is to transform the given problem into a mixed integer linear programming problem however the computational complexity of current mixed integer linear programming algorithms increases in the worst case exponentially as a function of the prediction horizon the focus of this paper is on making optimistic optimization suited to solve the given problem optimistic optimization is a class of algorithms that can find an approximation of the global optimum for general nonlinear optimization a key advantage of optimistic optimization is that one can specify the computational budget in advance and guarantee bounds on the suboptimality with respect to the global optimum we prove that optimistic optimization can be applied for the given problem by developing a dedicated semi metric and by proving it satisfies the necessary requirements for optimistic optimization moreover we show that the complexity of optimistic optimization is exponential in the control horizon instead of the prediction horizon hence using optimistic optimization is more efficient when the control horizon is small and the prediction horizon is large

technical communique an efficient algorithm for optimal control of pwa systems with polyhedral performance indices we present an algorithm for the computation of explicit optimal control laws for piecewise affine pwa systems with polyhedral performance indices the algorithm is based on dynamic programming dp and represents an extension of ideas initially proposed in kerrigan and mayne 2003 optimal control of constrained piecewise affine systems with bounded disturbances in proceedings of the 41st ieee conference on decision and control las vegas nevada usa december and baotic et al 2003 a new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index in proceedings of european control conference cambridge uk september specifically we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off line computations an extensive case study is provided which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature

optimal control of continuous time switched affine systems this paper deals with optimal control of switched piecewise affine autonomous systems where the objective is to minimize a performance index over an infinite time horizon we assume that the switching sequence has a finite length and that the decision variables are the switching instants and the sequence of operating modes we present two different approaches for solving such an optimal control problem the first approach iterates between a procedure that finds an optimal switching sequence of modes and a procedure that finds the optimal switching instants the second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur therefore providing a state feedback control law

an approximate solution for homogeneous boundary value problems with slowly varying coefficient matrices abstract in this paper an approximate closed form solution for homogeneous boundary value problems with slowly varying coefficient matrices is obtained the derivation of the approximate solution is based on the freezing technique which is commonly used in analyzing the stability of slowly varying initial value problems as well as solving them the error between the approximate and the exact solutions is given and an upper bound on the norm of the error is obtained this upper bound is proportional to the rate of change of the coefficient matrix of the boundary value problem the proposed approximate solution is obtained for a two point boundary value problem and is compared to its solution obtained numerically good agreement is observed between the approximate and the numerical solutions when the rate of change of the coefficient matrix is small

linear quadratic regulation of switched systems using informed policies the problem of designing a switching and control policy for regulating the state of a switched linear system to zero while minimizing a quadratic cost appears in numerous applications however obtaining the optimal policy is in general computationally intractable here we propose a class of suboptimal policies that exploit information in terms of upper or lower bounds on the optimal cost we analyze the performance of these novel policies obtaining new bounds on the optimal cost which are tighter than the initial ones the usefulness of these policies and performance bounds is illustrated in the context of resource aware control

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

sufficient conditions for stability of linear time varying systems abstract in this paper we consider sufficient conditions for the exponential stability of linear time varying systems of the form dot x t a t x t t 0 stability guaranteeing upper bounds for different measures of parameter variations are derived

dynamic programming for constrained optimal control of discrete time linear hybrid systems in this paper we study the solution to optimal control problems for constrained discrete time linear hybrid systems based on quadratic or linear performance criteria the aim of the paper is twofold first we give basic theoretical results on the structure of the optimal state feedback solution and of the value function second we describe how the state feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming

propositional logic in control and monitoring problems by using linear constraints on integer variables logical inference can be incorporated within model predictive control and model based detection problems resulting in mixed integer quadratic or mixed integer linear programming problems qualitative knowledge can be used to prioritize control objectives or to improve performance of detection schemes this article demonstrates some capabilities of combining logic using integer variables with quantitative models

stability and invariance analysis of uncertain discrete time piecewise affine systems this note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non invariant set x of states the approach relies on introducing fake dynamics outside x and on synthesizing a piecewise affine and possibly discontinuous lyapunov function via linear programming the existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in x the procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset x of the state space and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain x

hybrid state feedback stabilization with l 2 performance for discrete time switched linear systems in this paper the co design of continuous variable controllers and discrete event switching logics both in state feedback form is investigated for a class of discrete time switched linear control systems it is assumed that none of the subsystems is stabilized through a continuous state feedback alone however it is possible to stabilize the whole switched system via carefully designing both the continuous controllers and the switching logics sufficient synthesis conditions for this co design problem are proposed here in the form of bilinear matrix inequalities which is based on the argument of multiple lyapunov functions the closed loop switched system forms a special class of linear hybrid system and is shown to be asymptotically stable with a finite l 2 induced gain

on the input output representation of piecewise affine state space models this paper addresses the conversion of discrete time piecewise affine pwa state space models into input output form necessary and sufficient conditions for the existence of equivalent input output representations of a given pwa state space model are derived connections to the observability properties of pwa models are investigated under a technical assumption it is shown that every finite time observable pwa model admits an equivalent input output representation when an equivalent input output model exists a constructive procedure is presented to derive its equations several examples illustrate the proposed results

brief paper event driven optimization based control of hybrid systems with integral continuous time dynamics in this paper we introduce a class of continuous time hybrid dynamical systems called integral continuous time hybrid automata icha for which we propose an event driven optimization based control strategy events include both external actions applied to the system and changes of continuous dynamics mode switches the icha formalism subsumes a number of hybrid dynamical systems with practical interest e g linear hybrid automata different cost functions including minimum time and minimum effort criteria and constraints are examined in the event driven optimal control formulation this is translated into a finite dimensional mixed integer optimization problem in which the event instants and the corresponding values of the control input are the optimization variables as a consequence the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process a receding horizon control scheme exploiting the event based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite time or asymptotic convergence of the closed loop

response of linear slowly varying systems under external excitations abstract an approximate closed form solution for a linear slowly varying system under external excitation is derived the derivation of the solution is based on the technique of freezing slowly varying parameters a technique used in establishing the stability of slowly varying homogeneous systems the error between the approximate and exact solutions is given and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived approximate responses of two particular linear slowly varying systems under external excitation are obtained by the proposed technique good agreement between the approximate and numerically obtained solutions is observed

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

data based identification and control of nonlinear systems via piecewise affine approximation the piecewise affine pwa model represents an attractive model structure for approximating nonlinear systems in this paper a procedure for obtaining the pwa autoregressive exogenous arx autoregressive systems with exogenous inputs models of nonlinear systems is proposed two key parameters defining a pwarx model namely the parameters of locally affine subsystems and the partition of the regressor space are estimated the former through a least squares based identification method using multiple models and the latter using standard procedures such as neural network classifier or support vector machine classifier having obtained the pwarx model of the nonlinear system a controller is then derived to control the system for reference tracking both simulation and experimental studies show that the proposed algorithm can indeed provide accurate pwa approximation of nonlinear systems and the designed controller provides good tracking performance

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

optimal control of sampled data piecewise affine systems this paper discusses the optimal continuous time control problem of a class of piecewise affine pwa systems where the switching action of the discrete state is determined at each sampling time according to a condition on the continuous state such a system is called here the sampled data pwa sd pwa system first important remarks on the control design of this system via the continuous or discrete time pwa model are pointed out which motivate us to use the sd pwa model next based on the good properties of the proposed model an optimal continuous time controller of the sd pwa systems is proposed

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

control to facet by piecewise affine output feedback the control to facet problem plays an important role in the design of feedback controllers for piecewise affine hybrid systems on polytopes in the literature necessary conditions and sufficient conditions for solvability by static state feedback exist in this paper we extend these results to the case of continuous piecewise affine static output feedback for the construction of a controller a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the state polytope in the state feedback case the use of this special type of triangulation is not required

predictive control of switched nonlinear systems with scheduled mode transitions in this work a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times the main idea is to design a lyapunov based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed loop system this is achieved as follows for each constituent mode a lyapunov based model predictive controller mpc is designed and an analytic bounded controller using the same lyapunov function is used to explicitly characterize a set of initial conditions for which the mpc irrespective of the controller parameters is guaranteed to be feasible and hence stabilizing then constraints are incorporated in the mpc design which upon satisfaction ensure that 1 the state of the closed loop system at the time of the transition resides in the stability region of the mode that the system is switched into and 2 the lyapunov function for each mode is nonincreasing wherever the mode is reactivated thereby guaranteeing stability the proposed control method is demonstrated through application to a chemical process example

an efficient and stabilizing model predictive control of switched systems model predictive control mpc of switched systems typically requires an on line solution of a mixed integer program mip since the worst case complexity of the optimization problem increases exponentially with respect to the number of integer variables an on line implementation of the mpc for problems with large number of sub systems and or large horizons is usually expensive in this technical note we propose a stabilizing mpc formulation for state dependent switched systems that enables a tradeoff between the computational complexity of the mpc controller and the optimal performance of the closed loop system the proposed approach uses a pre terminal set in addition to the positively invariant terminal set which aids in reducing the on line complexity although at the expense of optimality examples are presented to illustrate the computational benefits of the proposed mpc strategy over existing mpc for switched systems

forces nlp an efficient implementation of interior point methods for multistage nonlinear nonconvex programs abstractreal time implementation of optimisation based control and trajectory planning can be very challenging for nonlinear systems as a result if an implementation based on a fixed linearisatio