Class Of Multiple-input Multiple-output Nonlinear Systems Research Articles

Synchronization Adaptive Fuzzy Gain Scheduling PID Controller for a Class of MIMO Nonlinear Systems

This paper presents a new Synchronization Adaptive Fuzzy Gain Scheduling PID controller (SAFGS-PIDc) for a class of Multiple-input multiple-output (MIMO) nonlinear systems with uncertainties. To achieve better adaptation properties, weighting factor is adapted to sum together the adaptive fuzzy control scheme and Fuzzy Gain Scheduler PID control (FGS-PIDc) method, such that both controllers can be incorporated at the same time. The FGS adjusts online the parameters of the conventional PID controller, and an Indirect Adaptive Fuzzy control (IAFc) scheme that uses feedback error function as inputs is constructed. In addition, each subsystem of MIMO system is able to adaptively compensate for uncertainties and external disturbance. Also, a robust control term is designed that aims to provide added robustness in the presence of uncertainties. The proposed scheme can overcome the controller singularity problem. While the proposed controller scheme requires the uncertainties to be bounded, it does not require this bound to be known. Thus, this control law can be used for the systems that the system’s models are quite unknown. The proposed method guarantees the stability of the closed-loop system based on Lyapunov theory. Finally, simulation studies demonstrate the usefulness and effectiveness of the proposed technique for controlling nonlinear.

Linear Parameter Varying Representation of a class of MIMO Nonlinear Systems

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying an LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, especially if a first principles based understanding of the system is unavailable. Converting a nonlinear model to an LPV form is also non-trivial and requires systematic methods to automate the process. Inspired by these challenges, a systematic LPV embedding approach starting from multiple-input multiple-output (MIMO) linear fractional representations with a nonlinear feedback block (NLFR) is proposed. This NLFR model class is embedded into the LPV model class by an automated factorization of the (possibly MIMO) static nonlinear block present in the model. As a result of the factorization, an LPV-LFR or an LPV state-space model with affine dependency on the scheduling is obtained. This approach facilitates the selection of the scheduling variable and the connected mapping of system variables. Such a conversion method enables to use nonlinear identification tools to estimate LPV models. The potential of the proposed approach is illustrated on a 2-DOF nonlinear mass-spring-damper example.

Online constrained optimization based adaptive robust control of a class of MIMO nonlinear systems with matched uncertainties and input/state constraints

A performance oriented two-loop control approach is proposed for a class of multiple-input–multiple-output (MIMO) systems with input saturation, state constraints, matched parametric uncertainties and input disturbances. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized to achieve the required robust tracking performances with respect to on-line replanned trajectory in the presence of input saturation and various types of matched uncertainties. In the outer loop, a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints. Interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Since the system in study is most appropriate to describe the dynamics of the robotic systems, the control of a two-axis planar robotic manipulator is used as an application example. Comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications.

Robust Adaptive Neural Control of a Class of MIMO Nonlinear Systems

In this paper we present a robust adaptive control for a class of uncertain continuous time multiple input multiple output (MIMO) nonlinear systems. Multiple multi-layer neural networks are employed to approximate the uncertainty of the nonlinear functions, and robustifying control terms are used to compensate for approximation errors. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability of the closed-loop system is guaranteed, and the tracking error asymptotically converges to zero. Simulations performed on a two-link robot manipulator illustrate the approach and its performance.