A unified numerical scheme for linear-quadratic optimal control problems with joint control and state constraints

Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W.P.M.H.

doi:10.1080/10556788.2011.593624

Cited by 16 publications

(8 citation statements)

References 69 publications

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“…The second part of Lemma 4 presents a method to achieve the aforementioned goal. The second part of Lemma 4 states that the optimal solution of QP ( 17) is unique and Lipschitz continuous in the RHS parameter w ∈ R a 1 + , and this result follows directly from proposition 4.1.d of Han et al (2012). A direct consequence of the second part of Lemma 4 is the following Lipschitz continuity result.…”

Section: Asymptotic Lower Boundmentioning

confidence: 70%

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

Özkan

2021

Stochastic Systems

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We study scheduling control of parallel processing networks in which some resources need to simultaneously collaborate to perform some activities and some resources multitask. Resource collaboration and multitasking give rise to synchronization constraints in resource scheduling when the resources are not divisible, that is, when the resources cannot be split. The synchronization constraints affect the system performance significantly. For example, because of those constraints, the system capacity can be strictly less than the capacity of the bottleneck resource. Furthermore, the resource scheduling decisions are not trivial under those constraints. For example, not all static prioritization policies retain the maximum system capacity, and the ones that retain the maximum system capacity do not necessarily minimize the delay (or, in general, the holding cost). We study optimal scheduling control of a class of parallel networks and propose a dynamic prioritization policy that retains the maximum system capacity and is asymptotically optimal in diffusion scale and a conventional heavy-traffic regime with respect to the expected discounted total holding cost objective.

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Section: Asymptotic Lower Boundmentioning

confidence: 70%

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

Özkan

2021

Stochastic Systems

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“…The general direct method approach to solving optimal control problems of convex. This is in contrast to the convex cost case where convergence to the true solution can be shown, for different direct solution methods [33][34][35][36][37][38]. We also note however that no general convergence proof for direct collocation methods of solving constrained optimal control problems exists in the literature.…”

Section: Effect Of Direct Transcription Methodsmentioning

confidence: 76%

Implications of discretization on dissipativity and economic model predictive control

Olanrewaju

Maciejowski

2017

Journal of Process Control

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Economic model predictive control, where a generic cost is employed as the objective function to be minimized, has recently gained much attention in model predictive control literature. Stability proof of the resulting closed-loop system is often based on strict dissipativity of the system with respect to the objective function. In this paper, starting with a continuous-time setup, we consider the 'discretize then optimize' approach to solving continuous-time optimal control problems and investigate the effect of the discretization process on the closedloop system. We show that while the continuous-time system may be strictly dissipative with respect to the objective function, it is possible that the resulting closed-loop system is unstable if the discrete-approximation of the continuoustime optimal control problem is not properly set up. We use a popular example from the economic MPC literature to illustrate our results.

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“…The optimisation problem that we address for (12) regards the minimization of the difference between the output voltage v(t) and a target periodic trajectory v r (t). Since, in practice, the inverter is controlled acting on the H-bridge switches, the problem can be tackled using two alternative approaches, as observed in [23].…”

Section: Optimisation Problem Formulationmentioning

confidence: 99%

“…Similarly to [5], in addition to the reference voltage v r on the capacitor, we define a corresponding reference current i r = C vr and we define the state of the system as x = [i − i r , v − v r ] T . Rewriting (12) in terms of x leads to a linear model of the form (1), with the following definitions for the system matrix, the input matrix and the excitation signal:…”

Section: Optimisation Problem Formulationmentioning

confidence: 99%

“…We consider a class of LQ optimal control problems [12] involving a steady-state oscillating linear dynamical system subject to a periodic excitation, a cost represented by a quadratic function of the system inputs and states, and linear inequality constraints on the state and/or the input. The dynamical system is asymptotically stable and described by:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quadratic Constrained Periodic Optimization for Bandlimited Linear Systems Via the Fourier-Based Method

Moretti

Zaccarian

Blanchini

2021

Journal of Dynamic Systems, Measurement, and Control

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Motivated by engineering applications, we address bounded steady-state optimal control of linear dynamical systems undergoing steady-state bandlimited periodic oscillations. The optimization can be cast as a minimization problem by expressing the state and the input as finite Fourier series expansions, and using the expansions coefficients as parameters to be optimized. With this parametrization, we address linear quadratic problems involving periodic bandlimited dynamics by using quadratic minimization with parametric time-dependent constraints. We hence investigate the implications of a discretization of linear continuous time constraints and propose an algorithm that provides a feasible suboptimal solution whose cost is arbitrarily close to the optimal cost for the original constrained steady-state problem. Finally, we discuss practical case studies that can be effectively tackled with the proposed framework, including optimal control of DC/AC power converters, and optimal energy harvesting from pulsating mechanical energy sources.

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A unified numerical scheme for linear-quadratic optimal control problems with joint control and state constraints

Cited by 16 publications

References 69 publications

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

Implications of discretization on dissipativity and economic model predictive control

Quadratic Constrained Periodic Optimization for Bandlimited Linear Systems Via the Fourier-Based Method

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