Decentralized finite-horizon suboptimal control for nonlinear interconnected dynamic systems using SDRE approach

Abstract

This paper introduces a new approach to ensure the decentralized horizon suboptimal control of interconnected nonlinear systems based on the decentralized finite-state-dependent Riccati equation. This approach is, in fact, a new extension of the state-dependent Riccati equation technique with a finite horizon for the case of large-scale nonlinear systems, which are characterized by the interconnection of n subsystems. The main finding in this work is the use of the Lyapunov direct method of stability analysis, associated with a quadratic function, in order to determine a new sufficient condition to guarantee the global asymptotic stability of the studied systems. We conducted advanced simulations of this new control method on three interconnected inverted pendulums. Our results demonstrate its efficiency and the sufficiency of the new stability conditions.

A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

“…The curves of Figure 3 show the evolution of the state variables of the interconnected system and the corresponding decentralized control signals evolution. Results of the state-dependent Riccati equation approach (Feydi et al, 2019) are depicted in the same figure. It can be seen that both decentralized approaches can counteract the effect of nonlinear interconnections.…”

“…Nonetheless, it is worth noting that our work has the merit to derive an explicit nonlinear state feedback controller that is more suitable for implementation. This is in contrast to the feedback controller in Feydi et al (2019), where the state-dependent matrices expressions solution of the differential Riccati equations are not determined, but obtained numerically with an iterative technique. This could be a major limitation in practice unless other steps are necessary for implementation, the complexity of which increases especially in a development environment other than MATLAB.…”

“…In the past few decades, several important research results on large-scale linear systems have been already published (Lefebvre et al, 1980; Mahmoud et al, 1985). These results, even though with a major theoretical contribution, encounter some limitations in practice since most of the real systems are inherently nonlinear; that is why there has been an increasing interest in developing control schemes for interconnected systems with linearities in their dynamics and/or interconnections (Attia et al, 2014; Dhbaibi et al, 2009; Feydi et al, 2019; Jamshidi and Wang, 1984; Rtibi et al, 2018; Tlili, 2017; Yoo et al, 2009).…”

Robust decentralized optimal stabilizability of continuous time uncertain interconnected systems: Application to large scale power system

“…Hence, many researchers proposed solutions to the problem of decentralized state or output feedback control of interconnected systems. [8][9][10][11][12] In fact, an important issue is to adapt methods with existing information structure constraints. So the best way is that each subsystem uses its own locally available information for control.…”

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

“…Since introducing decentralized control, it has been always considered an important control choice for interconnected systems. In this way, the decentralized optimal control partitions the measurement information and elaborates local and independent control law for each subsystem (Bakule, 2014; Feydi et al, 2019; Khorsand and Gattami, 2011; Mahmoud, 2011; Rtibi et al, 2017, 2018).…”