the distance to a polyhedron abstract we give some exact formulas and some estimates for the distance to a polyhedron in a normed linear space e we show that in the case when e r n endowed with the l norm these estimates are in general better than a recent estimate by cook gerards schrijver and tardos 2

control effort considerations in the stabilization of uncertain dynamical systems abstract this paper investigates the problem of designing a state feedback control to stabilize an uncertain nonlinear system we focus attention on the amplitude norm of the controller which is used to achieve this end the uncertain system is described by a state equation which contains uncertain parameters which are unknown but bounded a lyapunov function is used to establish the stability of the closed loop system the paper gives necessary and sufficient concitions for the uncertain system to be stabilizable with a given lyapunov function furthermore a procedure is indicated for the construction of the desired feedback control law

approximate primal solutions and rate analysis for dual subgradient methods in this paper we study methods for generating approximate primal solutions as a byproduct of subgradient methods applied to the lagrangian dual of a primal convex possibly nondifferentiable constrained optimization problem our work is motivated by constrained primal problems with a favorable dual problem structure that leads to efficient implementation of dual subgradient methods such as the recent resource allocation problems in large scale networks for such problems we propose and analyze dual subgradient methods that use averaging schemes to generate approximate primal optimal solutions these algorithms use a constant stepsize in view of its simplicity and practical significance we provide estimates on the primal infeasibility and primal suboptimality of the generated approximate primal solutions these estimates are given per iteration thus providing a basis for analyzing the trade offs between the desired level of error and the selection of the stepsize value our analysis relies on the slater condition and the inherited boundedness properties of the dual problem under this condition it also relies on the boundedness of subgradients which is ensured by assuming the compactness of the constraint set

the sharp lipschitz constants for feasible and optimal solutions of a perturbed linear program abstract the purpose of this paper is to derive the sharp lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right hand side perturbations the lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

l_p stabilization of integrator chains subject to input saturation using lyapunov based homogeneous design consider the n th integrator dot x j nx sigma u e n where x in mathbb r n u in mathbb r j n is the n th jordan block and e n 0 cdots 0 1 t in mathbb r n we provide easily implementable state feedback laws u k x which not only render the closed loop system globally asymptotically stable but also are finite gain l p stabilizing with arbitrarily small gain as in a saberi p hou and a stoorvogel ieee trans automat control 45 2000 pp 1042 1052 these l p stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite time stabilization of linear systems we also provide additional l infty stabilization results for the case of both internal and external disturbances of the n th integrator namely for the perturbed system dot x j nx e n sigma k x d d where d in mathbb r and d in mathbb r n

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

inverse optimality in robust stabilization the concept of a robust control lyapunov function bf rclf is introduced and it is shown that the existence of an bf rclf for a control affine system is equivalent to robust stabilizability via continuous state feedback this extends artstein s theorem on nonlinear stabilizability to systems with disturbances it is then shown that every bf rclf satisfies the steady state hamilton jacobi isaacs hji equation associated with a meaningful game and that every member of a class of pointwise min norm control laws is optimal for such a game these control laws have desirable properties of optimality and can be computed directly from the bf rclf without solving the hji equation for the upper value function

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

the structure of nonlinear elliptic equations on unbounded domains in dimensions 1 and 2 a probabilistic approach abstract suppose that d is an unbounded domain in r 2 with a compact boundary d and k x is a strictly positive holder continuous function on d such that x a log x a k x dx for some constant a 0 in this paper we study the nonlinear elliptic equation 1 2 u k x u x on d where 1 2 is a constant first we give explicit expressions in terms of super brownian motions for positive solutions of the above equation with the boundary conditions u d 0 and lim x u x log x c 0 c u d 0 when k behaves like x 2 log x l near for some constant l 1 in the one dimensional case we also have similar results

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

strong iiss for a class of systems under saturated feedback this paper proposes sufficient conditions under which nonlinear input affine systems can be made strongly iiss in the presence of actuator saturation strong iiss was recently proposed as a compromise between the strength of input to state stability iss and the generality of integral input to state stability iiss it ensures in particular that solutions are bounded provided that the disturbance magnitude is below a certain threshold and that they tend to the origin in response to any vanishing disturbance we propose a growth rate condition under which the bounded feedback law proposed by lin and sontag for disturbance free nonlinear systems ensures strong iiss in the presence of perturbations we illustrate our findings on the angular velocity control of a spacecraft with limited power thrusters in the specific case of linear time invariant systems with neutrally stable internal dynamics we provide a simple static state feedback that ensures strong iiss in presence of actuator saturations this second result is illustrated by the robust stabilization of the harmonic oscillator in both cases we provide an estimate of the maximum disturbance amplitude that can be tolerated without compromising solutions boundedness

simultaneous nonlinear model predictive control and state estimation an output feedback approach to model predictive control that combines state estimation and control into a single minmax optimization is introduced for discrete time nonlinear systems specifically a criterion that involves finite forward and backward horizons is minimized with respect to control input variables and is maximized with respect to the unknown initial state as well as disturbance and measurement noise variables under appropriate assumptions that encode controllability and observability we show that the state of the closed loop remains bounded and that a bound on tracking error can be found for trajectory tracking problems we also introduce a primaldual interior point method that can be used to efficiently solve the minmax optimization problem and show in simulation examples that the method succeeds even for severely nonlinear and non convex problems

a posteriori error bounds for the linearly constrained varitional inequality problem in this paper we derive a posteriori error bound of an approximate solution to a linearly constrained variational inequality problem three measures of error are used with each depending on a particular characterization of an exact solution and related to a certain class of iterative methods

application of a smoothing technique to decomposition in convex optimization dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure although the augmented lagrangian is computationally more stable than the ordinary lagrangian the ldquoprox termrdquo destroys the separability of the given problem in this technical note we use another approach to obtain a smooth lagrangian based on a smoothing technique developed by nesterov which preserves separability of the problem with this approach we derive a new decomposition method called ldquoproximal center algorithm rdquo which from the viewpoint of efficiency estimates improves the bounds on the number of iterations of the classical dual gradient scheme by an order of magnitude

computational complexity certification for dual gradient method application to embedded mpc abstract in this paper we analyze the computational complexity of the dual gradient method for solving linearly constrained convex problems when it is difficult to project on the primal feasible set described by linear constraints we use the lagrangian relaxation to handle the complicated constraints and then we apply the dual gradient algorithm for solving the corresponding dual we give a unified convergence rate analysis for the dual gradient algorithm we provide sublinear or linear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions our analysis relies on the lipschitz property of the dual function or an error bound property furthermore the iteration complexity analysis is based on two types of approximate primal solutions an average primal sequence or the last primal iterate sequence we also discuss complexity certifications and implementation aspects of the dual gradient algorithm on constrained mpc problems for embedded linear systems

asynchronous stochastic coordinate descent parallelism and convergence properties we describe an asynchronous parallel stochastic proximal coordinate descent algorithm for minimizing a composite objective function which consists of a smooth convex function added to a separable convex function in contrast to previous analyses our model of asynchronous computation accounts for the fact that components of the unknown vector may be written by some cores simultaneously with being read by others despite the complications arising from this possibility the method achieves a linear convergence rate on functions that satisfy an optimal strong convexity property and a sublinear rate 1 k on general convex functions near linear speedup on a multicore system can be expected if the number of processors is o n 1 4 we describe results from implementation on 10 cores of a multicore processor

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

viability control for a class of underactuated systems this paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained viability set k based on concepts from viability theory the necessary conditions for selecting viable controls for a nonholonomic system are given so that system trajectories starting in k always remain in k furthermore a class of state feedback control solutions for nonholonomic systems are redesigned by means of switching control so that system trajectories starting in k converge to a goal set g in k without ever leaving k the proposed approach can be applied in various problems whose objective can be recast as controlling a nonholonomic system so that the resulting trajectories remain forever in a subset k of the state space until they converge into a goal target set g in k the motion control for an underactuated marine vehicle in a constrained configuration set k is treated as a case study the set k essentially describes the limited sensing area of a vision based sensor system and viable control laws which establish convergence to a goal set g in k are constructed the robustness of the proposed control approach under a class of bounded external perturbations is also considered the efficacy of the methodology is demonstrated through simulation results

cooperative distributed model predictive control abstract in this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition the control strategy has the following features hard input constraints are satisfied terminating the iteration of the distributed controllers prior to convergence retains closed loop stability in the limit of iterating to convergence the control feedback is plantwide pareto optimal and equivalent to the centralized control solution no coordination layer is employed we provide guidance in how to partition the subsystems within the plant we first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class we also establish that under perturbation from a stable state estimator the origin remains exponentially stable for plants with sparsely coupled input constraints we provide an extension in which the decision variable space of each suboptimization is augmented to achieve pareto optimality we conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

nonlinear scaling of i iss lyapunov functions while nonlinear scalings of lyapunov functions are also lyapunov functions we provide examples that the same statement does not necessarily hold for input to state stable iss lyapunov functions or for integral iss iiss lyapunov functions we provide sufficient conditions under which a nonlinear scaling of an iss or iiss lyapunov function is also an iss or iiss lyapunov function we also introduce a generalization of the iiss lyapunov function which we term a dissipative iiss lyapunov function that allows for a larger class of nonlinear scalings so that nonlinear scalings of dissipative iiss lyapunov functions are again dissipative iiss lyapunov functions

a universal formula for stabilization with bounded controls abstract we provide a formula for stabilizing feedback law using a bounded control under the assumption that an appropriate control lyapunov function is known such a feedback smooth away from the origin and continuous everywhere is known to exist via artstein s theorem as in the unbounded control case treated in a previous note we provide an explicit and universal formula given by an algebraic function of lie derivatives in particular we extended to the bounded case the result that the feedback can be chosen analytic if the lyapunov function and the vector fields defining the system are analytic

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

a class of convergent primal dual subgradient algorithms for decomposable convex programs in this paper we develop a primal dual subgradient algorithm for preferably decomposable generally nondifferentiable convex programming problems under usual regularity conditions the algorithm employs a lagrangian dual function along with a suitable penalty function which satisfies a specified set of properties in order to generate a sequence of primal and dual iterates for which some subsequence converges to a pair of primal dual optimal solutions several classical types of penalty functions are shown to satisfy these specified properties a geometric convergence rate is established for the algorithm under some additional assumptions this approach has three principal advantages firstly both primal and dual solutions are available which prove to be useful in several contexts secondly the choice of step sizes which plays an important role in subgradient optimization is guided more determinably in this method via primal and dual information thirdly typical subgradient algorithms suffer from the lack of an appropriate stopping criterion and so the quality of the solution obtained after a finite number of steps is usually unknown in contrast by using the primal dual gap the proposed algorithm possesses a natural stopping criterion

metric selection in fast dual forward backward splitting the performance of fast forward backward splitting or equivalently fast proximal gradient methods depends on the conditioning of the optimization problem data this conditioning is related to a metric that is defined by the space on which the optimization problem is stated selecting a space on which the optimization data is better conditioned improves the performance of the algorithm in this paper we propose several methods with different computational complexity to find a space on which the algorithm performs well we evaluate the proposed metric selection procedures by comparing the performance to the case when the euclidean space is used for the most ill conditioned problem we consider the computational complexity is improved by two to three orders of magnitude we also report comparable to superior performance compared to state of the art optimization software

distributed model predictive control of linear discrete time systems with local and global constraints abstract this paper proposes a distributed model predictive control dmpc approach for a family of discrete time linear systems with local uncoupled and global coupled constraints the proposed approach is based on the dual problem of a mpc optimization problem involving all systems this dual problem is then distributedly solved based on the alternating direction multiplier method admm with several known simplifications when the network of systems is large or sparsely connected the computation of the optimal control using admm can be expensive the proposed approach mitigates this problem by allowing early termination of the admm process this is made possible via a finite time consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints under reasonable assumptions the approach is guaranteed to converge to a small neighborhood of the optimal so long as the network is connected recursive feasibility and exponential stability of the closed loop system are shown the performance of the proposed approach is demonstrated by a numerical example

linear convergence of randomized feasible descent methods under the weak strong convexity assumption in this paper we generalize the framework of the feasible descent method fdm to a randomized r fdm and a randomized coordinate wise feasible descent method rcfdm framework we show that many machine learning algorithms including the famous sdca algorithm for optimizing the svm dual problem or the stochastic coordinate descent method for the lasso problem fits into the framework of rc fdm we prove linear convergence for both r fdm and rc fdm under the weak strong convexity assumption moreover we show that the duality gap converges linearly for rc fdm which implies that the duality gap also converges linearly for sdca applied to the svm dual problem

a probabilistic approach to one class of nonlinear differential equations we establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes as an application we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations

approximate bisimulation relations for constrained linear systems in this paper we define the notion of approximate bisimulation relation between two continuous systems while exact bisimulation requires that the observations of two systems are and remain identical approximate bisimulation allows the observations to be different provided the distance between them remains bounded by some parameter called precision approximate bisimulation relations are conveniently defined as level sets of a so called bisimulation function which can be characterized using lyapunov like differential inequalities for a class of constrained linear systems we develop computationally effective characterizations of bisimulation functions that can be interpreted in terms of linear matrix inequalities and optimal values of static games we derive a method to evaluate the precision of the approximate bisimulation relation between a constrained linear system and its projection this method has been implemented in a matlab toolbox matisse an example of use of the toolbox in the context of safety verification is shown

on the convergence time of dual subgradient methods for strongly convex programs this paper studies the convergence time of dual gradient methods for general possibly nondifferentiable strongly convex programs for general convex programs the convergence time of dual subgradient gradient methods with simple running averages running averages started from iteration 0 is known to be o frac 1 epsilon 2 this paper shows that the convergence time for general strongly convex programs is o frac 1 epsilon this paper also considers a variation of the average scheme called the sliding running averages and shows that if the dual function of the strongly convex program is locally quadratic then the convergence time of the dual gradient method with sliding running averages is o log frac 1 epsilon the convergence time analysis is further verified by numerical experiments

certainty equivalence implies detectability abstract it is shown that any stabilizing certainty equivalence control used within an adaptive control system causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator s output error e p for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend the fact that certainty equivalence implies detectability has been known for some time this has been shown to be so whenever the process model is linear and the controller and estimator models are also linear for every frozen value of p in this paper use is made of recently introduced concepts of input to state stability and detectability for nonlinear systems to prove that the same implication is valid in a more general nonlinear setting

rate analysis of inexact dual first order methods application to dual decomposition we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex problems the complicating constraints are moved into the cost using the lagrange multipliers the dual problem is solved by inexact first order methods based on approximate gradients for which we prove sublinear rate of convergence in particular we provide a complete rate analysis and estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions moreover we solve approximately the inner problems with a linearly convergent parallel coordinate descent algorithm our analysis relies on the lipschitz property of the dual function and inexact dual gradients further we combine these methods with dual decomposition and constraint tightening and apply this framework to linear model predictive control obtaining a suboptimal and feasible control scheme

the gain scheduling and the robust state feedback stabilization problems we consider dynamical uncertain systems of the form x spl dot a x w b x w u where w t spl isin w is an unknown but bounded time varying parameter we consider the robust state feedback stabilization problem in which we consider a control of the form u spl phi x and the gain scheduling stabilization problem in which a control of the form u spl phi x w full information control is admitted we show that for convex processes those systems in which for fixed x the set of all a x w b x w is convex the two problems are equivalent i e if there exists a locally lipschitz gain scheduling stabilizing control then there exists a robustly stabilizing control continuous everywhere except possibly at the origin thus for convex process stabilization knowledge of w t is not an advantage for the compensator then we consider the special class of polytopic lpv systems and show that there is no loss of regularity as in the general case if we pass from a gain scheduling controller to a state feedback controller in particular no discontinuity at the origin may occur we show that the existence of a dynamic controller always implies the existence of a static one finally we show that we can always find a linear gain scheduling controller for a stabilizable system this means that a possible advantage of the online measurement of the parameter w t is that this always allows for linear compensators whose implementation can be easier than that of nonlinear ones

lagrangian relaxation via ballstep subgradient methods we exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value augmented with simple averaging schemes they asymptotically find objective and constraint subgradients involved in optimality conditions when applied to lagrangian relaxation of convex programs they find both primal and dual solutions and have practicable stopping criteria up until now similar results have only been known for proximal bundle methods and for subgradient methods with divergent series stepsizes whose convergence can be slow encouraging numerical results are presented for large scale nonlinear multicommodity network flow problems

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

on linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems in this paper we propose a fully distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence in particular we prove that under the assumption of strong convexity and lipschitz continuity of the gradient of the primal objective function we have a global error bound type property for the dual problem using this error bound property we devise a fully distributed dual gradient scheme i e a gradient scheme based on a weighted step size for which we derive global linear rate of convergence for both dual and primal suboptimality and for primal feasibility violation numerical simulations are also provided to confirm our theory

simultaneous stabilization for a collection of single input nonlinear systems this paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single input nonlinear systems the control lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time invariant simultaneously stabilizing state feedback controllers additionally a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented for any collection of second order and third order feedback linearizable systems in canonical form global simultaneous stabilization via a single state feedback controller is shown to be always possible two examples are included for illustration

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

global asymptotic controllability implies input to state stabilization the main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable gac control affine systems that render the closed loop systems input to state stable iss with respect to actuator errors extensions for fully nonlinear gac systems with actuator errors are also discussed our controllers have the property that they tolerate small observation noise as well