Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples

Bitmead, Robert R.; Gevers, Michel; Petersen, Ian R.; Kaye, R.J.

doi:10.1016/0167-6911(85)90027-1

Cited by 119 publications

(57 citation statements)

References 8 publications

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“…k=O 1 subject to the system dynamics (I), and constraint (2). Similar to the infinite horizon case, we define JN(xO) = oo when the constraints are infeasible over the horizon length N .…”

Section: Finite Horizon Formulationmentioning

confidence: 99%

“…Minimize the infinite horizon cost: subject to the system dynamics (I), and constraint (2). When it is impossible to satisfy the constraints (2) over the infinite horizon from the initial state xo, we will resort to the convention of defining J(xo) = m.…”

Section: Infinite Horizon Formulationmentioning

confidence: 99%

“…Even when no constraints are present, stability and performance analysis of receding horizon implementations can be quite involved [7,8,2, 31. The addition of end constraints (a constraint that the state be zero at the end of the output horizon) can be used to greatly simplify the analysis, but the addition of these constraints usually lacks justification or physical motivation.…”

Section: Introductionmentioning

confidence: 99%

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Constrained finite receding horizon linear quadratic control

Primbs

Nevistic

Proceedings of the 36th IEEE Conference on Decision and Control

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Issues of feasibility, stability and performance are considered for a finite horizon formulation of receding horizon control (RHC) for linear systems under mixed linear state and control constraints. It is shown that for a sufficiently long horizon, a receding horizon policy will remain feasible and result in stability, even when no end constraint is imposed. In addition, offline finite horizon calculations can be used to determine not only a stabilizing horizon length, but guaranteed performance bounds for the receding horizon policy. These calculations are demonstrated on two examples.

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“…k=O 1 subject to the system dynamics (I), and constraint (2). Similar to the infinite horizon case, we define JN(xO) = oo when the constraints are infeasible over the horizon length N .…”

Section: Finite Horizon Formulationmentioning

confidence: 99%

Section: Infinite Horizon Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constrained finite receding horizon linear quadratic control

Primbs

Nevistic

Proceedings of the 36th IEEE Conference on Decision and Control

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“…This requirement is certainly undesirable from a practical point of view, especially when the control horizon N is small. In [13] it has been shown that stability is achieved for E = Q where Q is the observability gramian of (1). If E = with the unique non-negative definite steady-state solution (i.e.…”

Section: Consider the Recursionsmentioning

confidence: 99%

End-point parametrization and guaranteed stability for a model predictive control scheme

Weiland¹,

Stoorvogel²,

Tiagounov³

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)

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In this paper we consider the closed-loop asymptotic stability of the model predictive control scheme which involves the minimization of a quadratic criterion with a varying weight on the end-point state. In particular, we investigate the stability properties of the (MPC-) controlled system as function of the end-point penalty and provide a useful parametrization of the class of end-point penalties for which stability of the controlled system can be guaranteed. The results are successfully applied for the implementation of an MPC controller of a binary distillation process.

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“…In this paper we will analyze the stability properties of the controlled system as function of the end-point penalty of the criterion function. The effect of finite end-point penalties on the stability of receding horizon schemes has been investigated in [1,12] for discrete time systems and in [7,9,12] for continuous time systems. all these papers provide sufficient conditions for stability of controlled systems based on monotonicity results of Riccati equations and linear matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%