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A Novel Low-Conservative Constrained H∞ Model Predictive Control for Linear Switched Systems

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Abstract

The problem of unacceptable conservatism and the lack of disturbance consideration are important research gaps for model predictive control (MPC) schemes in linear switched systems (LSSs). To solve these challenges, this study develops, for the first time, an organized strategy of MPC and persistent dwell time (PDT) structure for LSSs through multiple Lyapunov functions (MLFs) to dramatically reduce conservatism. Additionally, exogenous perturbations are considered in the system dynamics, and the H∞ performance is ensured to reduce the effects of the perturbations. Assuming the input constraints as well as the aforementioned assumptions, the proposed scheme is designed through MLFs, and asymptotic stability is proved. Finally, the effectiveness of the suggested strategy for the target systems is investigated through the numerical simulation of two examples. The simulation results suggest the stated strategy for real systems.

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Abbreviations

\(a_{s}\) :

Variation rate of Lyapunov function

\(b\) :

Limiting factor of Lyapunov function at switching moments

\(\varepsilon_{k}\) :

Maximum limit of cost function

\(n\) :

Persistent dwell time

\(m\) :

Persistent duration

\(C\) :

Total number of switching in \(m\)-sub-interval

r :

Switching rate in \(m\)-sub-interval

\(\gamma_{h}\) :

Disturbance rejection level

\(q_{\max }\) :

Maximum limit of disturbance energy

\(u_{eu,\max }\) :

Maximum limit of eu-th component of input

\(s_{es,\max }\) :

Maximum limit of the eu-th component within the state

\(\Pi_{\sigma (k)}\) :

Control gain

\(h\) :

Predictive horizon

\(J_{\sigma (k)}\) :

Cost function

\(f_{\sigma (k)}\) :

Lyapunov function

\(\Theta_{\sigma (k)}\) :

Matrix describing Lyapunov function

\(\Sigma_{\sigma (k)}\), \(\Delta_{\sigma (k)}\), \({\rm T}_{\sigma (k)}\), and \(\Omega_{\sigma (k)}\) :

Variables in optimization problem

\(\sigma (k)\) :

Switching signal

\(G_{\sigma \left( k \right)} ,H_{\sigma \left( k \right)} ,V_{\sigma \left( k \right)}\), \(W_{\sigma \left( k \right)}\) and \(N_{\sigma \left( k \right)}\) :

State space matrices

\(s(k)\) :

State

\(u(k)\) :

Input

\(q(k)\) :

Disturbance

\(d(k)\) :

Controlled output

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  1. College of Mechanical and Electrical Engineering, Guangzhou Institute of Technology, Guangzhou, 510075, Guangdong, China

    Yuancheng Xie

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  1. Yuancheng Xie
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Xie, Y. A Novel Low-Conservative Constrained H∞ Model Predictive Control for Linear Switched Systems. J. Inst. Eng. India Ser. B (2024). https://doi.org/10.1007/s40031-024-01068-1

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