Generalized predictive control of linear time-varying systems

Li, Zheng; Wang, Guoli

doi:10.1016/j.jfranklin.2016.10.021

Cited by 18 publications

(20 citation statements)

References 33 publications

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“…In this setting an online learner iteratively picks an action 𝑦 𝑡 and then suffers a convex hitting cost 𝑓 𝑡 (𝑦 𝑡 ) and a (linear) switching cost 𝑐 (𝑦 𝑡 , 𝑦 𝑡 −1 , • • • , 𝑦 𝑡 −𝑝 ), depending on current and previous 𝑝 actions. This type of online optimization with memory has deep connections to convex body chasing [5,9,10,27] and has wide applications in areas such as power systems [6,19,21], electric vehicle charging [14,19], cloud computing [11,12,25], and online control [16,20,22,24,31].…”

Section: Introductionmentioning

confidence: 99%

Online Optimization with Feedback Delay and Nonlinear Switching Cost

Pan

Shi

Lin

et al. 2022

Proc. ACM Meas. Anal. Comput. Syst.

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We study a variant of online optimization in which the learner receives k-rounddelayed feedback about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a nonlinear manner. Our main result shows that a novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has a constant, dimension-free competitive ratio that is $O(L^2k )$, where L is the Lipschitz constant of the switching cost. Additionally, we provide lower bounds that illustrate the Lipschitz condition is required and the dependencies on k and L are tight. Finally, via reductions, we show that this setting is closely related to online control problems with delay, nonlinear dynamics, and adversarial disturbances, where iROBD directly offers constant-competitive online policies.

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Section: Introductionmentioning

confidence: 99%

Online Optimization with Feedback Delay and Nonlinear Switching Cost

Pan

Shi

Lin

et al. 2022

Proc. ACM Meas. Anal. Comput. Syst.

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“…The generalized predictive control (GPC) algorithm, as a special case of MPC methods, incorporates multi-step prediction and receding horizon optimization of MPC algorithms and can be effectively applied to systems with large inertia and time-delay [18]. Moreover, it also enables self-tuning capability and feedback rectification, thereby easily adapting to uncertainty of environmental interference and inaccurate modeling [19]. Although GPC has been successfully verified in tracking the pre-set trajectory of controlling target, time-consuming characteristics and computational intensity cannot be tolerant due to recursive calculation of the so-called Diophantine equation and numerous matrix multiplications [20].…”

Section: Introductionmentioning

confidence: 99%

Design of an Improved Implicit Generalized Predictive Controller for Temperature Control Systems

et al. 2020

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In this study, an implicit proportional-integral-based generalized predictive controller (PIGPC) is proposed to effectively control temperatures of industrial systems with time-varying delay. The controller is designed to optimize the target function with the proportional-integral structure for improving the controlling performance of implicit PIGPC. Meanwhile, the recursive least square method is leveraged to directly identify the parameters of controller. Compared with the conventional implicit generalized predictive controller, the process of parameter identification converges faster. The Lagrange multiplier method is introduced to solve the optimal control law of implicit PIGPC by considering the input constraints of system. An approximate decoupling controller for multivariable systems is proposed to eliminate the coupling effects. Simulation and experimental results manifest the effectiveness and feasibility of the proposed controller in temperature control systems. INDEX TERMS Decoupling control, input constraint, proportional-integral generalized predictive controller (PIGPC), Lagrange multiplier method, temperature control system.

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“…Since the pioneering work of Richalet et al [13], many predictive control methods have been developed, e.g. generalised predictive control (GPC) [14], predictive functional control (PFC) [15] and dynamic matrix control [16].…”

Section: Introductionmentioning

confidence: 99%