Model Predictive Control for Linear Parameter Varying Systems Using Parameter Dependent Lyapunov Function

Wada, Nobutaka; Saito, Koji; Saeki, Masami

doi:10.1109/tcsii.2006.883832

Cited by 87 publications

(91 citation statements)

References 16 publications

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“…Since the optimal control problem (6) explicitly requires that the input u(t) = u ⋆ 0|t and state x(t + 1) = x ⋆ 1|t satisfy constraints (6c), Theorem 3 means that the model predictive controller (7) guarantees constraint satisfaction for any initial state x(t), mode (t), and remaining dwell-time (t) in the domain of the controller. The following corollary characterizes the domain of the MPC (7). Corollary 2.…”

Section: Long-horizon Mpcmentioning

confidence: 99%

“…Let  0|t =  0|t be compact switch-RCI sets. Then, MPC (7) is defined for all initial states x(t), modes (t), and times t ∈ N in the initial condition set (3).…”

Section: Long-horizon Mpcmentioning

confidence: 99%

“…According to Corollary 2, if the terminal sets  0|t =  ∞ 0|t are the maximal switch-RCI sets, then MPC (7) guarantees constraint satisfaction for every initial condition for which it is possible to satisfy constraints. Thus, in terms of constraint satisfaction, MPC (7) has no conservativeness.…”

Section: Long-horizon Mpcmentioning

confidence: 99%

“…In particular, linear switched systems can be modeled as polytopic linear parameter varying systems. [7][8][9][10][11] For nonlinear switched systems with constraints, the viability theory 12 can be used to characterize the set of states for which there exists a controller that enforces constraint satisfaction. However, many results from viability theory are nonconstructive, whereas this paper includes a computationally efficient algorithm for computing the viability domain of the switched system and a model predictive controller for realizing constraint enforcement.…”

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Danielson

Bridgeman

Cairano

2019

Intl J Robust & Nonlinear

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Summary This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of control invariant sets for switched constrained systems, called switch–robust control invariant (switch‐RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell‐time and admissible mode transitions. These switch‐RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control‐law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell‐time. The switch‐RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed‐loop constraint satisfaction for switched constrained systems. We show that our controller is nonconservative in the sense that it enforces constraints on the largest possible domain, ie, constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch‐RCI sets are demonstrated on a vehicle lane‐changing case study.

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Section: Long-horizon Mpcmentioning

confidence: 99%

“…Let  0|t =  0|t be compact switch-RCI sets. Then, MPC (7) is defined for all initial states x(t), modes (t), and times t ∈ N in the initial condition set (3).…”

Section: Long-horizon Mpcmentioning

confidence: 99%

Section: Long-horizon Mpcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Danielson

Bridgeman

Cairano

2019

Intl J Robust & Nonlinear

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“…Hence, robust MPC (RMPC) for those non-ideal systems is of more theoretical and practical significance [1,2]. One class of systems that take into account the uncertainties are the so-called linear parameter varying (LPV) systems [3,4].Papers investigating RMPC of LPV systems can be found in [5][6][7], and more recently [8][9][10][11], and so on. The results of these papers were developed based on the assumption that system states are always measurable.…”

mentioning

confidence: 99%

An optimal approach to output-feedback robust model predictive control of LPV systems with disturbances

Yang¹,

Gao²,

Feng

et al. 2016

Int. J. Robust. Nonlinear Control

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Summary An observer‐based output feedback predictive control approach is proposed for linear parameter varying systems with norm‐bounded external disturbances. Sufficient and necessary robust positively invariant set conditions of the state estimation error are developed to determine the minimal ellipsoidal robust positively invariant set and observer gain through offline computation. The quadratic upper bound of state estimation error is updated and included in an ℋ∞‐type cost function of predictive control to optimize transient output feedback control performance. Recursive feasibility of the dynamic convex optimization problem is guaranteed in the proposed predictive control strategy. With the input‐to‐state stable observer, the closed‐loop control system states are steered into a bounded set. Simulation results are given to demonstrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.

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The Stochastic Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

Hajiloo¹,

Xie²

2014

Asian Journal of Control

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This paper considers robust model predictive control (RMPC) methods for a linear parameter varying (LPV) system that has both probabilistic uncertain and time-varying parameters. The parameters are considered to be measured online. In this regard, the aircraft landing gear system is considered as an LPV system whose parameters variation can affect both stability and performance. By transforming this system into a convex combination of linear time-invariant vertices form with the tensor-product (TP) model transformation method, the landing gear system is represented as a polytopic linear parameter-varying system. A computationally efficient RMPC control signal law is calculated online by carrying out the convex optimization involving linear matrix inequalities (LMIs) in MPC which leads to finding the solutions that can guarantee the closed-loop robust stability and performance. The proposed controller can effectively suppress the shimmy vibration of the landing gear with variable taxiing velocity and wheel caster length, also with the probabilistic uncertain torsional spring stiffness.

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Model Predictive Control for Linear Parameter Varying Systems Using Parameter Dependent Lyapunov Function

Cited by 87 publications

References 16 publications

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

An optimal approach to output-feedback robust model predictive control of LPV systems with disturbances

The Stochastic Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

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