Sliding Mode Control for a Class of Nonlinear Systems with a Quadratic Input Form

Xu, Sendren Sheng Dong; Liang, Yew-Wen

doi:10.1166/jctn.2013.3087

Cited by 7 publications

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“…Theorem 4.1 tells us that when the objective function is linear the optimal controls are bang‐bang for the optimal control problem subject to a linear descriptor noncausal system. The input of the noncausal system is linear in Section 4, while the quadratic input form can be found in a number of practical cases such as power system models studied in [34] and it also attracted the attentions of some researchers at a theoretical level [35]. These results concerning quadratic input form inspired me to investigate an optimal control problem for a descriptor noncausal system with quadratic input variables as the following:

({, \begin{matrix} left \\ array J (0, x (0), x (L)) = \sup_{\begin{matrix} u false(i false) \in U_{a d} \\ 0 \leq i \leq L \end{matrix}} \sum_{j = 0}^{L} r_{j}^{T} x (j) \\ array subject to \\ array E x (j + 1) = A x (j) + B u (j) + D u^{2} (j), \\ array j = 0, 1, 2, \dots, L - 1, \end{matrix})

where r j ∈ R n , j =0,1,2,…, L are known coefficient vectors, and u ( j )∈ U ad =[−1,1], j =0,1,2,…, L −1.…”

Section: Optimal Control Problem Of Descriptor Noncausal System With Quadratic Input Variablesmentioning

confidence: 99%

Optimal Control for Discrete‐time Descriptor Noncausal Systems

Shu

2020

Asian Journal of Control

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In this paper, optimal control problems governed by linear discrete-time descriptor noncausal systems (with quadratic input variables) are investigated in order.A descriptor system assumed to be regular alone is called descriptor noncausal system. According to Bellman's principle of optimality in dynamic programming, a recurrence equation for simplifying the optimal control problems is derived. Then, employing the recurrence equation, a bang-bang optimal control problem subject to a linear descriptor noncausal system and an optimal control problem subject to a descriptor noncausal system with quadratic input variables are both settled, and the optimal solutions are given through exact expressions.A numerical example is presented to illustrate the effectiveness of the results obtained concerning the bang-bang optimal control problem.

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({, \begin{matrix} left \\ array J (0, x (0), x (L)) = \sup_{\begin{matrix} u false(i false) \in U_{a d} \\ 0 \leq i \leq L \end{matrix}} \sum_{j = 0}^{L} r_{j}^{T} x (j) \\ array subject to \\ array E x (j + 1) = A x (j) + B u (j) + D u^{2} (j), \\ array j = 0, 1, 2, \dots, L - 1, \end{matrix})

where r j ∈ R n , j =0,1,2,…, L are known coefficient vectors, and u ( j )∈ U ad =[−1,1], j =0,1,2,…, L −1.…”

Section: Optimal Control Problem Of Descriptor Noncausal System With Quadratic Input Variablesmentioning

confidence: 99%

Optimal Control for Discrete‐time Descriptor Noncausal Systems

Shu

2020

Asian Journal of Control

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“…It has many advantages such as fast response, small sensitivity to system uncertainties and/or disturbances from the environment, and being easily designed. Based on these reasons, the CSMC approach has been popularly applied to a variety of control issues [1][2][3][27][28][29][30][31][32][33][34][35][36][37][38][39]. The design of CSMC is known to consist of two main steps.…”

Section: Introductionmentioning

confidence: 99%

Super-Twisting-Algorithm-Based Terminal Sliding Mode Control for a Bioreactor System

2014

Abstract and Applied Analysis

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This study proposes a class of super-twisting-algorithm-based (STA-based) terminal sliding mode control (TSMC) for a bioreactor system with second-order type dynamics. TSMC not only can retain the advantages of conventional sliding mode control (CSMC), including easy implementation, robustness to disturbances, and fast response, but also can make the system states converge to the equivalent point in a finite amount of time after the system states intersect the sliding surface. The chattering phenomena in TSMC will originally exist on the sliding surface after the system states achieve the sliding surface and before the system states reach the equivalent point. However, by using the super twisting algorithm (STA), the chattering phenomena can be obviously reduced. The proposed method is also compared with two other methods: (1) CSMC without STA and (2) TSMC without STA. Finally, the control schemes are applied to the control of a bioreactor system to illustrate the effectiveness and applicability. Simulation results show that it can achieve better performance by using the proposed method.

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Optimal control for uncertain discrete-time singular systems under expected value criterion

Shu

Zhu

2020

Fuzzy Optim Decis Making

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Sliding Mode Control for a Class of Nonlinear Systems with a Quadratic Input Form

Cited by 7 publications

References 0 publications

Optimal Control for Discrete‐time Descriptor Noncausal Systems

Optimal Control for Discrete‐time Descriptor Noncausal Systems

Super-Twisting-Algorithm-Based Terminal Sliding Mode Control for a Bioreactor System

Optimal control for uncertain discrete-time singular systems under expected value criterion

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