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Rate Constrained Discrete-time Maximum Principle⁎Siddhartha Ganguly and Souvik Das are supported by the PMRF grant RSPMRF0262 and RSPMRF0262, from the Ministry of Human Resource Development, Govt. of India, respectively. The work of one of the authors was also partially supported by a sponsored project from the Indian Space Research Organization. The authors are with Systems and Control Engineering, IIT Bombay. Issue 19 (2021)
Record Type:
Journal Article
Title:
Rate Constrained Discrete-time Maximum Principle⁎Siddhartha Ganguly and Souvik Das are supported by the PMRF grant RSPMRF0262 and RSPMRF0262, from the Ministry of Human Resource Development, Govt. of India, respectively. The work of one of the authors was also partially supported by a sponsored project from the Indian Space Research Organization. The authors are with Systems and Control Engineering, IIT Bombay. Issue 19 (2021)
Main Title:
Rate Constrained Discrete-time Maximum Principle⁎Siddhartha Ganguly and Souvik Das are supported by the PMRF grant RSPMRF0262 and RSPMRF0262, from the Ministry of Human Resource Development, Govt. of India, respectively. The work of one of the authors was also partially supported by a sponsored project from the Indian Space Research Organization. The authors are with Systems and Control Engineering, IIT Bombay.
Abstract: Actuators in real-world systems operate under limited bandwidth and saturation constraints. Mathematically, these limitations manifest as certain types of constraints being imposed on the sequence of control action. While saturation constraints have been studied extensively, bandwidth limitations in the actuators have received very little attention in the control community. While an attempt has been made in the direction of incorporating frequency constraints at the synthesis stage, rate constraints on the control at the design stage has not been studied extensively in the regime of discrete-time. This article tries to fill in that gap by incorporating rate constraints on the control trajectories. We propose a new discrete-time Pontryagin maximum principle (PMP) with rate constraints being imposed on the control and derive a set of first order necessary conditions for optimality. As an illustration, the linear quadratic (LQ) optimal control problem under rate constraints has been considered.