Controller design for nonlinear quadratic Markov jumping systems with input saturation

International audience

In this note, we deal with the stability and stabilization problems for nonlinear quadratic discrete-time periodic systems. By using the quadratic Lyapunov function, and a so called periodic invariant set, delay-independent sufficient conditions for local stability and local stabilization for nonlinear quadratic discrete-time periodic systems are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

Observer-based Adaptive Controller Design for Nonlinear Saturation Systems With Output Constraints

Observer-based control for time-delayed quasi-one-sided Lipschitz nonlinear systems under input saturation

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

This paper addresses the local stabilization problem of SISO nonlinear quadratic discrete-time systems subject to logarithmic quantization. The sector bound approach is applied to derive LMI-based conditions for synthesizing a stabilizing linear controller (both state and dynamic output feedback) while either maximizing the set of initial states assuming a given quantizer or minimizing the quantization density for a given set of initial states. A numerical example is presented to illustrate the application of the derived results.

A relation between the output regulation and the observer design for nonlinear systems

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the "explosion of complexity", the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Reduced-order observer-based control design for nonlinear stochastic systems

Fixed-time control design for nonlinear uncertain systems via adaptive method

Finite-time controller design of multiple integrator nonlinear systems with input saturation

This paper focuses on an input-to-state practical stability (ISpS) problem of nonlinear systems which possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances. The dynamic disturbances depend on the states and the measured output of the system, and its assumption conditions are relaxed compared with the common restrictions. Based on an input-driven filter, fuzzy logic systems are directly used to approximate the unknown and desired control signals instead of the unknown nonlinear functions, and an integrated backstepping technique is used to design an adaptive output-feedback controller that ensures robustness with respect to unknown parameters and uncertain nonlinearities. This paper, by applying the ISpS theory and the generalized small-gain approach, shows that the proposed adaptive fuzzy controller guarantees the closed-loop system being semi-globally uniformly ultimately bounded. A main advantage of the proposed controller is that it contains only three adaptive parameters that need to be updated online, no matter how many states there are in the systems. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

This article is concerned with the tracking control problem for uncertain high-order nonlinear systems in the presence of input saturation. A finite-time control strategy combined with neural state observer and command filtered backstepping is proposed. The neural network models the unknown nonlinear dynamics, the finite-time command filter (FTCF) guarantees the approximation of its output to the derivative of virtual control signal in finite time at the backstepping procedure, and the fraction power-based error compensation system compensates for the filtering errors between FTCF and virtual signal. In addition, the input saturation problem is dealt with by introducing the auxiliary system. Overall, it is shown that the designed controller drives the output tracking error to the desired neighborhood of the origin at a finite time and all the signals in the closed-loop system are bounded at a finite time. Two simulation examples are given to demonstrate the control effectiveness.

In this paper, an adaptive neural networks &#x0028 NNs &#x0029 tracking controller is proposed for a class of single-input &#x002F single-output &#x0028 SISO &#x0029 non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real &#x0028 SPR &#x0029 theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.