Model predictive control: for want of a local control Lyapunov function, all is not lost

Grimm, G.; Messina, Michael J.; Tuna, S. Emre; Teel, Andrew R.

doi:10.1109/tac.2005.847055

Cited by 226 publications

(351 citation statements)

References 22 publications

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“…In this paper we study stability and recursive feasibility of nonlinear MPC schemes without stabilizing terminal constraints or costs. For such schemes, it is known that stability for sufficiently large optimization horizons can be deduced from controllability assumptions or -alternatively and almost equivalently -bounds on the optimal value functions, see Jadbabaie and Hauser (2005); Grimm et al (2005); Tuna et al (2006); Grüne (2009) ;Grüne et al (2010); Grüne and Pannek (2011);Worthmann (2011).…”

Section: Introductionmentioning

confidence: 99%

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Boccia

Grüne

Worthmann

2014

Systems & Control Letters

139

122

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In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N .For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel.

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Section: Introductionmentioning

confidence: 99%

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Boccia

Grüne

Worthmann

2014

Systems & Control Letters

139

122

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“…then it follows from [1] that the theoretical bound M * 1 for the necessary prediction horizon decreases which was confirmed in our numerical simulations. Remark 3.3 Explicit bounds to guarantee the stability properties of the underlying discrete-time system can be found in [1].…”

Section: Stability and Inverse Optimalitysupporting

confidence: 81%

“…also Remark 4.1, below. To conclude semiglobal asymptotical stability of the closed loop system using the proposed MPC controller we present the following theorem, which relies on Theorem 1 in [1]. Theorem 3.1 (Stability) Suppose the following conditions hold: 1. l and F are continuous; 2.…”

Section: Stability and Inverse Optimalitymentioning

confidence: 99%

“…Make use of the underlying discrete-time system via Theorem 1 in [1] and Theorem 1 in [10], see [13] for details. Therefore one can apply the calculated MPC control coming out of an approximated model in reality without loss of stability.…”

Section: Stability and Inverse Optimalitymentioning

confidence: 99%

“…Remark 3.3 Explicit bounds to guarantee the stability properties of the underlying discrete-time system can be found in [1]. In order to show inverse optimality of our approach we suppose that F is such that there exists a closed set X f ⊂ R 2n and a control law u = u f (ξ, x) with , u f (ξ, x)), H(X)) is ∈ X f .…”

Section: Stability and Inverse Optimalitymentioning

confidence: 99%

See 2 more Smart Citations

Model Predictive Control for Nonlinear Sampled-Data Systems

Grüne

Nešić

Pannek

Assessment and Future Directions of Nonlinear Model Predictive Control

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Summary. The topic of this paper is a new model predictive control (MPC) approach for the sampled-data implementation of continuous-time stabilizing feedback laws. The given continuous-time feedback controller is used to generate a reference trajectory which we track numerically using a sampled-data controller via an MPC strategy. Here our goal is to minimize the mismatch between the reference solution and the trajectory under control. We summarize the necessary theoretical results, discuss several aspects of the numerical implemenation and illustrate the algorithm by an example.

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Carleman approximation based quasi‐analytic model predictive control for nonlinear systems

Fang

Armaou

2016

AIChE Journal

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This manuscript aims at developing a nonlinear model predictive controller formulation based on Carleman approximation. It approximates the nonlinear dynamic constraints with polynomial ones through Taylor expansion. Then, it extends the state variables to higher orders following the Kronecker product rule and expresses the nonlinear dynamic constraints with an extended bilinear representation. With little loss of nonlinear information, the formulation enables analytical prediction of future states. It also analytically calculates the sensitivity of the cost function to the manipulated inputs to facilitate the search algorithm by serving as the gradient. We present a brief analysis of error accumulation caused by Carleman approximation and then improve the accuracy of the approach by resetting extended states periodically. The idea of efficient temporal discretization is embedded in control vector parameterization to improve the controller performance. The advantages are illustrated in two applications where we solve a tracking problem and a regulation problem.

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Model predictive control: for want of a local control Lyapunov function, all is not lost

Cited by 226 publications

References 22 publications

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Model Predictive Control for Nonlinear Sampled-Data Systems

Carleman approximation based quasi‐analytic model predictive control for nonlinear systems

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