Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

Abstract

This paper investigates the optimization of a general class of nonlinear singularly perturbed systems. Tensor productbased modeling, algebraic properties, and singular perturbation theory played a significant role in the formulation of the derived reduced model. The obtained reduced output is a nonlinear state and input dependent vector. In this case, solving the optimal control problem when minimizing a quadratic performance index becomes more difficult because the weighting matrices vary as functions of states. So the reformulation of the initial problem is needed and the resolution is discussed from an analytical point of view. A two-step controller design procedure is suggested and an algorithm is proposed for the calculus of the gain matrices of the nonlinear control law. The Simulation results are presented to demonstrate the effectiveness of the approach and the power of the implemented algorithm.

Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

“…In addition, [13] established a strategy for the single-input and single-output nonlinear systems in strict-feedback form, while taking into account both the fault-tolerant and the optimal control. Meanwhile, the optimal control of the singular systems which include more fruitful information is also worth studying [14,15]. For example, [14] designed the optimal controller of nonlinear singular perturbed systems based on the tensor algebra framework.…”

“…Meanwhile, the optimal control of the singular systems which include more fruitful information is also worth studying [14,15]. For example, [14] designed the optimal controller of nonlinear singular perturbed systems based on the tensor algebra framework. About the complex singular systems in [15], the optimal controller was achieved by utilizing the robust adaptive dynamic programming method.…”

“…Since the time-varying and nonlinear systems are more suitable for the actual physical systems than the simple systems, the systems with the nonlinear or time-varying or both characteristics are considered in [3,6,8]. However, the research of time-varying nonlinear (TVN) systems will be more complex and challenging than the simple systems, not to mention the optimal control for such systems [4,14]. In order to make the optimal control of TVN systems have a better effect, an effective strategy should be proposed [10][11][12][13][14].…”

Robust control design for the FLEXOP demonstrator aircraft via tensor product models

“…In addition, the higher‐order singular values give a possibility for trade‐off between the accuracy and complexity of the resulting model. TP model applications are given in [25‐29].…”

Tensor product model transformation‐based control for fractional‐order biological pest control systems

“…Further development and related studies which enhance the performance of the TPMT in various aspect were presented in resent previous works [21,25,30,35,40–47]. TPMT method has been employed in various engineering applications from benchmark dynamical systems such as TORA systems [33,48], magnetic levitation systems [49], three‐tank liquid level control systems [50] to the complex systems such as, aircraft and hypersonic vehicle systems [25,51–53], crane systems [54,55], and robots [26,56].…”