An optimal PID controller design for nonlinear constrained optimal control problems

Li, Bin; Teo, Kok Lay; Lim, Cheng‐Chew; Duan, Guang Ren

doi:10.3934/dcdsb.2011.16.1101

Cited by 23 publications

(22 citation statements)

References 10 publications

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“…Such systems have randomly jumping parameters, and the jumps are modeled by the transitions of a Markov chain. Because of the capacity of capturing the abrupt mode changes for the plant, Markovian jump system has a wide range of application in such areas as power system load control [7] and ship steering for course changing and course keeping [8].…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered control for networked Markovian jump systems

Wang

Shi

Lim

et al. 2014

Intl J Robust & Nonlinear

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134

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SUMMARYThe problem of H 1 control for networked Markovian jump system under event-triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event-triggered scheme to choose the transmitted data is designed. A Markovian jump time-delay system model is employed to describe the event-triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed-loop system is stable and has a prescribed performance index. A co-design method for the H 1 controller and the event-triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example.

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Section: Introductionmentioning

confidence: 99%

Event‐triggered control for networked Markovian jump systems

Wang

Shi

Lim

et al. 2014

Intl J Robust & Nonlinear

Self Cite

134

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“…The Riccati PDEs, on the other hand, are usually not in standard form and thus cannot be solved using off-the-shelf software packages. The approach proposed in this paper can be viewed as an extension of optimization-based PID tuning ideas (see [3], [6], [14], [18]) to infinite dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization

Ren

Lin

et al. 2015

2015 American Control Conference (ACC)

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This paper proposes a new control synthesis approach for the stabilization of boundary-controlled parabolic partial differential equations (PDEs). In the proposed approach, the optimal boundary control is expressed in integral state feedback form with quadratic kernel function, where the quadratic's coefficients are decision variables to be optimized. We introduce a system cost functional to penalize both state and kernel magnitude, and then derive the cost functional's gradient in terms of the solution of an auxiliary "costate" PDE. On this basis, the output stabilization problem can be solved using gradient-based optimization techniques such as sequential quadratic programming. The resulting optimal boundary control is guaranteed to yield closed-loop stability under mild conditions. The primary advantage of our new approach is that the costate PDE is in standard form and can be solved easily using the finite difference method. In contrast, the traditional control synthesis approaches for boundary-controlled parabolic PDEs (i.e., the LQ control and backstepping approaches) require solving nonstandard Riccati-type and Klein-Gorden-type PDEs.

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“…Nevertheless, some partial attempts have been made in the literature. In [10], for example, an optimal PID controller is derived by solving an optimization problem in which the feedback gains are decision variables. This problem contains continuous inequality constraints that arise because of engineering specifications on the controller, such as bounds on the overshoot and rise time.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we consider a general optimal control problem in which a feedback controller of given structure is optimized by varying certain adjustable parameters. Unlike in [10,29], we do not restrict ourselves to any particular control structure or any particular system-our problem is completely general. We first formulate the optimal feedback control problem as a semiinfinite optimization problem in which the adjustable control parameters are decision variables.…”

Section: Introductionmentioning

confidence: 99%

“…We then show how to solve this semi-infinite optimization problem using a recently-developed exact penalty method, which has proven to be very effective at handling semi-infinite and discrete constraints [26,27]. This exact penalty approach has two key advantages over the constraint transcription method used in [10]: (i) it involves one approximation parameter instead of two; and (ii) it is guaranteed to converge to a local optimal solution (in contrast, the constraint transcription method is only guaranteed to converge if the global solution is obtained at each step, which is unlikely in practice). We demonstrate the effectiveness of our new exact penalty approach by applying it to the optimal control of a hang glider.…”

Section: Introductionmentioning

confidence: 99%

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Optimal feedback control for dynamic systems with state constraints: An exact penalty approach

et al. 2013

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In this paper, we consider a class of nonlinear dynamic systems with terminal state and continuous inequality constraints. Our aim is to design an optimal feedback controller that minimizes total system cost and ensures satisfaction of all constraints. We first formulate this problem as a semi-infinite optimization problem. We then show that by using a new exact penalty approach, this semi-infinite optimization problem can be converted into a sequence of nonlinear programming problems, each of which can be solved using standard gradient-based optimization methods. We conclude the paper by discussing applications of our work to glider control.

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An optimal PID controller design for nonlinear constrained optimal control problems

Cited by 23 publications

References 10 publications

Event‐triggered control for networked Markovian jump systems

Event‐triggered control for networked Markovian jump systems

Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization

Optimal feedback control for dynamic systems with state constraints: An exact penalty approach

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