Zhitao Liu

Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance

In this technical note, we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance. By using backstepping approaches, two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a Nussbaum function. The Nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation. Unlike some existing control schemes for systems with input saturation, the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance. Besides showing global stability, transient performance is also established and can be adjusted by tuning certain design parameters.

Robust Adaptive Failure Compensation of Hysteretic Actuators for a Class of Uncertain Nonlinear Systems

Hysteresis exists in a wide range of physical actuators. Furthermore, such actuators may be subject to failures or faults which are often uncertain in time, value and pattern during system operation. However, the available results based on adaptive approaches to compensate for unknown failures of hysteretic actuators are very limited. The work of this note is aimed at addressing such a problem by considering controlling a class of strict feedback systems. A scheme designing smooth adaptive control is proposed for this purpose. It is shown that the designed adaptive controller can ensure all signals are bounded and the tracking error asymptotically approaches a pre-defined bound, no matter whether the hysteretic actuators operate in normal or faulty modes.

Output feedback control for uncertain nonlinear systems with input quantization

In this paper, we propose a new adaptive output-feedback tracking control scheme for a class of uncertain nonlinear systems with input quantized by a newly-proposed quantizer. This quantizer is a combination of a logarithmic (or a hysteresis) quantizer and a uniform quantizer, and it has the advantages of both logarithmic and uniform quantizers in ensuring reducible communication expenses and acceptable quantization errors for better system performances. Compared with existing results in adaptive control, the proposed scheme provides a way to relax certain restrictive conditions, in addition to solving the problem of adaptive output-feedback control with input quantization. It is shown that the designed adaptive controller ensures global boundedness of all the signals in the closed-loop system and enables the tracking error to exponentially converge towards a compact set which is adjustable.

Event-Triggered Adaptive Control for a Class of Uncertain Nonlinear Systems

In this technical note, the problem of event-trigger based adaptive control for a class of uncertain nonlinear systems is considered. The nonlinearities of the system are not required to be globally Lipschitz. Since the system contains unknown parameters, it is a difficult task to check the assumption of the input-to-state stability (ISS) with respect to the measurement errors, which is required in most existing literature. To solve this problem, we design both the adaptive controller and the triggering event at the same time such that the ISS assumption is no longer needed. In addition to presenting new design methodologies based on the fixed threshold strategy and relative threshold strategy, we also propose a new strategy named the switching threshold strategy. It is shown that the proposed control schemes guarantee that all the closed-loop signals are globally bounded and the tracking/stabilization error exponentially converges towards a compact set which is adjustable.

Technical communique: Asymptotic Lyapunov stability with probability one of quasi-integrable Hamiltonian systems with delayed feedback control

The asymptotic Lyapunov stability with probability one of multi-degree-of-freedom (MDOF) quasi-integrable and nonresonant Hamiltonian systems with time-delayed feedback control subject to multiplicative (parametric) excitation of Gaussian white noise is studied. First, the time-delayed feedback control forces are expressed approximately in terms of the system state variables without time delay and the system is converted into ordinary quasi-integrable and nonresonant Hamiltonian system. Then, the averaged Ito stochastic differential equations are derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems and the expression for the largest Lyapunov exponent of the linearized averaged Ito equations is derived. Finally, the necessary and sufficient condition for the asymptotic Lyapunov stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent to be negative. An example is worked out in detail to illustrate the above mentioned procedure and its validity and to show the effect of the time delay in feedback control on the largest Lyapunov exponent and the stability of the system.

Robust adaptive failure compensation of hysteretic actuators for parametric strict feedback systems

It is well known that hysteresis often exists and failures may occur in practical actuators during system operation. The compensation for uncertainties caused by unknown hysteresis and unknown failures is an important problem in ensuring system stability and performances. However, available results based on adaptive approaches to address such a problem are still very limited. In this paper, an adaptive tracking control scheme is proposed to solve such a problem. Simulation results also illustrate the effectiveness of the control scheme.

Control via interconnection and damping assignment of linear time-invariant systems: a tutorial

Interconnection and damping assignment is a controller design methodology that regulates the behaviour of dynamical systems assigning a desired port-Hamiltonian structure to the closed-loop. A key step for the application of the method is the solution of the so-called matching equation that, in the case of nonlinear systems, is a partial differential equation. It has recently been shown that for linear systems the problem boils down to the solution of a linear matrix inequality that, moreover, is feasible if and only if the system is stabilisable – making the method universally applicable. It has also been shown that if we narrow the class of assignable structures – e.g. to mechanical instead of the larger port-Hamiltonian – the problem is still translated to a linear matrix inequality, but now stabilisability is not sufficient to ensure its feasibility. It is additionally required that the uncontrolled modes are simple and lie on the jω axis, which is consistent with the considered scenario of mechanical systems without friction. The purpose of this article is to present these important results in a tutorial, self-contained form – invoking only basic linear algebra methods.

Stabilisation of nonlinear chemical processes via dynamic power-shaping passivity-based control

It is well known that energy-balancing passivity-based control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, some authors have used power-shaping techniques, where stabilisation is achieved by shaping a function akin to power instead of energy. Some extensions of the techniques to general nonlinear systems, yielding static state-feedback control laws, have also been reported. In this article, we extend these techniques to dynamic feedback control and apply them to nonlinear chemical processes. The stability analysis is carried out using the shaped power function as Lyapunov function. The proposed technique is illustrated with two nonlinear chemical process examples.

Event-Based Consensus for Linear Multiagent Systems Without Continuous Communication

In this paper, we propose a new distributed event-trigger consensus protocol for linear multiagent systems with external disturbances. Two consensus problems are considered: one is a leader-follower case and the other is a nonleader case. Different from the existing results, our proposed scheme enables each agent to decide when to transmit its state signals to its neighbors such that continuous communication between neighboring agents is avoided. Clearly, this can largely decrease the communication burden of the whole communication network. Besides, since the control signal for each agent is discontinuous because of the event-triggering mechanism, the existence of a solution for the closed-loop system in the classical sense may not be guaranteed. To solve this problem, we employ a nonsmooth analysis technique including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, it is shown that uniformly bounded consensus results are derived and the bound of the consensus error is adjustable by choosing suitable design parameters.In this paper, we propose a new distributed event-trigger consensus protocol for linear multiagent systems with external disturbances. Two consensus problems are considered: one is a leader–follower case and the other is a nonleader case. Different from the existing results, our proposed scheme enables each agent to decide when to transmit its state signals to its neighbors such that continuous communication between neighboring agents is avoided. Clearly, this can largely decrease the communication burden of the whole communication network. Besides, since the control signal for each agent is discontinuous because of the event-triggering mechanism, the existence of a solution for the closed-loop system in the classical sense may not be guaranteed. To solve this problem, we employ a nonsmooth analysis technique including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, it is shown that uniformly bounded consensus results are derived and the bound of the consensus error is adjustable by choosing suitable design parameters.

Adaptive failure compensation of hysteric actuators in controlling uncertain nonlinear systems

Hysteresis nonlinearity exists in many physical actuators and actuator failures seem inevitable in practice. However, there is still no result available to compensate for failures of hysteric actuators in the design of controllers based on adaptive approaches. In this paper, we address such a problem by considering controlling a class of unknown nonlinear systems with multiple hysteric actuators. Two schemes are presented to design control signals for these actuators. Both schemes can accommodate uncertain patterns, values and time of actuator failures, in addition to system parametric uncertainties. It is shown that the designed controllers can compensate for failure and hysteresis effects of the actuators in the sense that system stability and tracking performance are maintained no matter whether this is any actuator failure or not.