Optimal control of hybrid switched systems: A brief survey

Zhu, Feng; Antsaklis, Panos J.

doi:10.1007/s10626-014-0187-5

Cited by 172 publications

(87 citation statements)

References 90 publications

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“…The finite horizon optimal control problem is more tractable [19], [20]. For a survey on the recent results in the optimal control of switched and hybrid systems, see [21].…”

Section: A Related Workmentioning

confidence: 99%

Optimal control with regular objectives using an abstraction-refinement approach

Leong

Prabhakar

2016

2016 American Control Conference (ACC)

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Abstract-This paper presents a method to synthesize a sequence of control inputs for a discrete-time switched linear system equipped with a cost function, such that the controlled system behavior satisfies a linear-time temporal objective with minimal cost. An abstract finite state weighted transition system is constructed, such that the cost of the optimal control on the abstract system provides an upper bound on the cost of the optimal control for the original system. Specifically, the abstract system is constructed from finite partitions of the state and input spaces by solving certain optimization problems, and a sequence of controllers is obtained by considering a sequence of uniformly refined partitions. Under mild assumptions on the optimal control for the switched system, the costs of the sequence of controllers constructed converges to the cost of the optimal control for the switched system. The abstraction refinement algorithm is implemented in the tool OptCAR. The feasibility of this approach is illustrated on two different examples, by constructing automatically, sub-optimal controllers with improving optimal costs.

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“…The finite horizon optimal control problem is more tractable [19], [20]. For a survey on the recent results in the optimal control of switched and hybrid systems, see [21].…”

Section: A Related Workmentioning

confidence: 99%

Optimal control with regular objectives using an abstraction-refinement approach

Leong

Prabhakar

2016

2016 American Control Conference (ACC)

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“…, , , , , , 1,2,3... , [12] and the bi-diagonalizing in QR iteration [13] which can be easily applied to calculating solution such as DSP and so on, several effective TDOA closed localization algorithms have been developed since [4]. The typical algorithms are the spherical-interpolation [4], Chan [6], linear-correction least squares (LCLS) [7] and constrained total least squares (CTLS) [1], et al Before discussing the SQP algorithm, the description of the linear model is given below.…”

Section: Closed Localization Algorithm and Sqp Solution Based Least Smentioning

confidence: 99%

“…SDR technology [16] is one way to solve it. The solution gained by taking out the rank 1 constraint can be regarded as suboptimal or used as the starting point for other algorithms, although it is not the optimal solution for Equation (12). Because the estimation accuracy of SDR is not enough (discussed in details in simulation part), a SQP-based algorithm is give below.…”

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confidence: 99%

A Novel TDOA-Based Localization Algorithm Using Sequential Quadratic Programming

Liu¹,

Huang²,

Wang³

2016

IJHIT

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“…Concerning the optimal control for this type of system, there are the works of Xu and Antsaklis (to find the optimal switching instants for switched autonomous systems using nonlinear optimization techniques), Egerstedt et al (same object as in the work of Xu and Antsaklis but with a different optimization method), Rinehart et al (to design the discrete‐time state‐feedback controllers for continuous‐time switched homogeneous systems) for instance. A survey of the optimal control of hybrid switched systems has been presented in the work of Zhu and Antsaklis . Some fruitful results on the stabilization of switched hyperbolic system in an infinite‐dimensional way have been reported; see, eg, the papers of Amin et al, Prieur et al, and the survey paper of Yang et al More recently, Huang and Xiang addressed the problem of stability analysis in the 2D nonlinear continuous‐time switched systems.…”

Section: Introductionmentioning

confidence: 99%

Calculus of variations approach for state and parameter estimation in switched 1D hyperbolic PDEs

Nguyen

Duby

Besançon

2018

Optim Control Appl Methods

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Summary This paper proposes the use of calculus of variations to solve the problem of state and parameter estimation for a class of switched 1‐dimensional hyperbolic partial differential equations coupled with an ordinary differential equation. The term “switched” here refers to a system changing its characteristics according to a switching rule, which may depend on time, parameters of the system, and/or state of the system. The estimation method is based on a smooth approximation of the system dynamics and the use of variational calculus on an augmented Lagrangian cost functional to get the sensitivity with respect to the initial state and some (possibly distributed) parameters of the system. Those sensitivities or variations, together with related adjoint systems, are used as inputs for an optimization algorithm to identify the values of the variables to be estimated. Two examples are provided to demonstrate the effectiveness of the proposed method. The first one is concerned with a switched overland flow model, developed from Saint‐Venant equations and Green‐Ampt law; the second example deals with a switched free traffic flow model based on the Lighthill‐Whitham‐Richards representation, modified by the presence of a relief route.

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Optimal control of hybrid switched systems: A brief survey

Cited by 172 publications

References 90 publications

Optimal control with regular objectives using an abstraction-refinement approach

Optimal control with regular objectives using an abstraction-refinement approach

A Novel TDOA-Based Localization Algorithm Using Sequential Quadratic Programming

Calculus of variations approach for state and parameter estimation in switched 1D hyperbolic PDEs

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