Global Stabilization of Triangular Systems with Time-Delayed Dynamic Input Perturbations

A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal uncertain strict-feedback-like subsystem, the input signal to which is generated by an uncertain nonlinear input unmodeled dynamics that is driven by the entire system state (including unmeasured state variables) and is also allowed to depend on time delayed versions of the system state variable and control input signals. The system also includes additive uncertain nonlinear functions, coupled nonlinear appended dynamics, and uncertain dynamic input nonlinearities with time-varying uncertain time delays. The proposed control design approach provides a globally stabilizing delay-independent robust adaptive output-feedback dynamic controller based on a dual dynamic high-gain scaling based structure.Comment: 2017 IEEE International Carpathian Control Conference (ICCC

Lyapunov-based Control Design For Uncertain Mimo Systems

In this dissertation. we document the progress in the control design for a class of MIMO nonlinear uncertain system from five papers. In the first part, we address the problem of adaptive control design for a class of multi-input multi-output (MIMO) nonlinear systems. A Lypaunov based singularity free control law, which compensates for parametric uncertainty in both the drift vector and the input gain matrix, is proposed under the mild assumption that the signs of the leading minors of the control input gain matrix are known. Lyapunov analysis shows global uniform ultimate boundedness (GUUB) result for the tracking error under full state feedback (FSFB). Under the restriction that only the output vector is available for measurement, an output feedback (OFB) controller is designed based on a standard high gain observer (HGO) stability under OFB is fostered by the uniformity of the FSFB solution. Simulation results for both FSFB and OFB controllers demonstrate the efcacy of the MIMO control design in the classical 2-DOF robot manipulator model. In the second part, an adaptive feedback control is designed for a class of MIMO nonlinear systems containing parametric uncertainty in both the drift vector and the input gain matrix, which is assumed to be full-rank and non-symmetric in general. Based on an SDU decomposition of the gain matrix, a singularity-free adaptive tracking control law is proposed that is shown to be globally asymptotically stable (GAS) under full-state feedback. iii Output feedback results are facilitated via the use of a high-gain observer (HGO). Under output feedback control, ultimate boundedness of the error signals is obtained the size of the bound is related to the size of the uncertainty in the parameters. An explicit upper bound is also provided on the size of the HGO gain constant. In third part, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The full-state feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the ef cacy of the multi-input multioutput control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and post utter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller. In the fourth part, a continuous robust feedback control is designed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with two degrees of freedom containing unstructured nonlinear uncertainties in the drift vector and parametric uncertainties in the high frequency gain matrix, which is allowed to be non-symmetric in general. Given some mild assumptions on the system model, a singularity-free continuous robust tracking coniv trol law is designed that is shown to be semi-globally asymptotically stable under full-state feedback through a Lyapunov stability analysis. The performance of the proposed algorithm have been verified on a two-link robot manipulator model and 2-DOF aeroelastic model

Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty

Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers

Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying

New control strategies for neuroprosthetic systems

The availability of techniques to artificially excite paralyzed muscles opens enormous potential for restoring both upper and lower extremity movements with\ud neuroprostheses. Neuroprostheses must stimulate muscle, and control and regulate the artificial movements produced. Control methods to accomplish these tasks include feedforward (open-loop), feedback, and adaptive control. Feedforward control requires a great deal of information about the biomechanical behavior of the limb. For the upper extremity, an artificial motor program was developed to provide such movement program input to a neuroprosthesis. In lower extremity control, one group achieved their best results by attempting to meet naturally perceived gait objectives rather than to follow an exact joint angle trajectory. Adaptive feedforward control, as implemented in the cycleto-cycle controller, gave good compensation for the gradual decrease in performance observed with open-loop control. A neural network controller was able to control its system to customize stimulation parameters in order to generate a desired output trajectory in a given individual and to maintain tracking performance in the presence of muscle fatigue. The authors believe that practical FNS control systems must\ud exhibit many of these features of neurophysiological systems

Incremental generalized homogeneity, observer design and semiglobal stabilization

The notion of incremental generalized homogeneity is introduced, giving new results on semiglobal stabilization by output feedback and observer design and putting into a unifying framework the stabilization design for triangular (feedback/ feedforward) and homogeneous systems. A state feedback controller and an asymptotic state observer are designed separately by dominating the generalized homogeneity degree of the nonlinearities with the degree of the linear approximation of the system and an output feedback controller is obtained according to a certainty-equivalence principle

On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper