Uncertain Nonlinear Multi-input Multi-output Systems Research Articles

Fuzzy Observer Constraint Based on Adaptive Control for Uncertain Nonlinear MIMO Systems With Time-Varying State Constraints.

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.

Adaptive Fuzzy Tracking Control Based Barrier Functions of Uncertain Nonlinear MIMO Systems With Full-State Constraints and Applications to Chemical Process

An adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi-input multi-output (MIMO) systems is presented in this paper. This class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets. The properties of the system structure are inevitable to bring about a complicated design and a difficult task. The fuzzy logic systems are employed to approximate the unknown functions of systems, and the decoupling backstepping way is proposed to design the stability controller and adaptation laws. Barrier Lyapunov functions (BLFs) are constructed in the backstepping design to guarantee that the constraint bounds are not violated. Based on Lyapunov analysis in barrier form, we can prove the stability of the closed-loop system. Two simulation examples are viewed to verify the feasibility of the approach.

Robust adaptive NN control for a class of uncertain discrete-time nonlinear MIMO systems

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.

λ1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

AbstractWe address the problem of tracking for a general class of uncertain nonlinear MIMO systems with input quantization, without requiring any matching conditions. We consider the λ1 adaptive controller and analyze its performance bounds in the presence of input quantization. We study two common types of quantization, the uniform quantization and the logarithmic quantization. In both cases we provide the transient performance bounds, which are decoupled into two positive terms. One of these terms can be made arbitrarily small by increasing the rate of adaptation, while the other term can be made small by increasing the quantization density. The performance bounds imply that with sufficiently dense quantization and fast adaptation, the output of an uncertain MIMO nonlinear system can follow the desired reference input sufficiently closely. We notice that with λ1 adaptive control architecture fast adaptation does not lead to high-gain control and retains guaranteed time-delay margin, which is bounded away from zero. Simulations included in the paper illustrate the results.

L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

AbstractWe address the problem of tracking for a general class of uncertain nonlinear MIMO systems with input quantization, without requiring any matching conditions. We consider the 1 adaptive controller and analyze its performance bounds in the presence of input quantization. We study two common types of quantization, the uniform quantization and the logarithmic quantization. In both cases we provide the transient performance bounds, which are decoupled into two positive terms. One of these terms can be made arbitrarily small by increasing the rate of adaptation, while the other term can be made small by increasing the quantization density. The performance bounds imply that with sufficiently dense quantization and fast adaptation, the output of an uncertain MIMO nonlinear system can follow the desired reference input sufficiently closely. We notice that with L1 adaptive control architecture fast adaptation does not lead to high-gain control and retains guaranteed time-delay margin, which is bounded away from zero. Simulations included in the paper illustrate the results.