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

Discrete-Time Neural Network Output Feedback Control of Nonlinear Systems in Non-Strict Feedback Form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which is represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: 1) a NN observer to estimate the system states with the input-output data, and 2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem in the discrete-time backstepping design is avoided by using the universal NN approximator. The persistence excitation (PE) condition is relaxed both in the NN observer and NN controller design. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is shown

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy

Adaptive output regulation for a class of nonlinear systems with guaranteed transient performance

This paper is dedicated to adaptive output regulation for a class of nonlinear systems with asymptotic output tracking and guarantee of prescribed transient performance. With the employment of internal model principle, we first transform this problem into a specific adaptive stabilization problem with output constraints. Then, by integrating the time-varying Barrier Lyapunov Function (BLF) technique together with the high gain feedback method, we develop an output-based control law to solve the constrained stabilization problem and consequently confine the output tracking error to a predefined arbitrary region. The output-based control law enables adaptive output regulation in the sense that, under unknown exosystem dynamics, all the closed-loop system signals are bounded whilst the controlled output constraints are not violated. Finally, efficacy of the proposed design is illustrated through a simulation example

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated. The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the Kalman-Yakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller. A numerical example based on a scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The 6 degree-of-freedom nonlinear vehicle model is linearized, giving the design model for which the controller is synthesized. The adaptive output feedback controller is then applied to an evaluation model, which is nonlinear, coupled, and includes actuator dynamics, and is shown to result in stable tracking in the presence of uncertainties that destabilize the baseline linear output feedback controller.This research is funded by the Air Force Research Laboratory/Aerospace Systems Directorate grant FA 8650-07-2-3744 for the Michigan/MIT/AFRL Collaborative Center in Control Sciences and the Boeing Strategic University Initiative. Approved for Public Release; Distribution Unlimited. Case Number 88ABW- 2014-2551

Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems

A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach

Adaptive neural control of MIMO nonlinear systems with a block-triangular pure-feedback control structure

This paper presents adaptive neural tracking control for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. All subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. To deal with the nonaffine appearance of the control variables, the mean value theorem (MVT) is employed to transform the systems into a block-triangular strict-feedback form with control coefficients being couplings among various inputs and outputs. A systematic procedure is proposed for the design of a new singularityfree adaptive neural tracking control strategy. Such a design procedure can remove the couplings among subsystems and hence avoids the possible circular control construction problem. As a consequence, all the signals in the closed-loop system are guaranteed to be semiglobally uniformly ultimately bounded (SGUUB). Moreover, the outputs of the systems are ensured to converge to a small neighborhood of the desired trajectories. Simulation studies verify the theoretical findings revealed in this work

Reinforcement Learning Based Dual-Control Methodology for Complex Nonlinear Discrete-Time Systems with Application to Spark Engine EGR Operation

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach

Global Practical Tracking by Output Feedback for Nonlinear Systems with Unknown Growth Rate and Time Delay

This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results

Nonlinear control and its application to active tilting-pad bearings

The drawbacks of active magnetic bearings are arousing interest in the adaptation of mechanical bearings for active use. A promising mechanical bearing candidate for active operation is the tilting-pad bearing. In this research, we introduce an active tilting-pad bearing with linear actuators that translate each pad. The use of feedback in determining the actuator forces allows for the automatic, continuous adjustment of the pad position during the machine operation. In this work, we develop the dynamic model of the active bearing system such that the actuator forces are the control inputs. The hydrodynamic force is modeled as a spring/damper-like force with unknown damping and stiffness coefficients. Whereas in the literature, the damping and stiffness effects are normally considered linear, here, motivated by a numerical study based on the Reynolds equation, we use a nonlinear model for the stiffness force. An adaptive controller is designed to asymptotically regulate the rotor to the bearing center. The proposed control design is applicable to both the linear and nonlinear stiffness models. Simulations and experiments show that the active strategy improves the bearing performance in comparison to its traditional passive operation. Further, the experiments indicate the nonlinear stiffness-based controller slightly improves the active bearing regulation performance relative to the linear-based one. To the best of our knowledge, this dissertation is the first to report the experimental demonstration of an active tilting-pad bearing using feedback control. Since the model of the active tilting-pad bearing has a parametric strict-feedback-like form, the second part of this dissertation is dedicated to constructing new nonlinear control tools for this class of systems. Specifically, we consider the regulation and tracking control problems for multi-input/multi-output parametric strict-feedback systems in the presence of additive, exogenous disturbances and parametric uncertainties. For such systems, robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation. In this work, under the assumption the disturbances are C2 with bounded time derivatives; we present a new C0 robust adaptive control construction that guarantees the output/tracking error is asymptotically driven to zero. Numerical examples illustrate the main results, including cases where the disturbances do not satisfy the aforementioned assumptions