George A. Rovithakis

Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance

A novel robust adaptive controller for multi-input multi-output (MIMO) feedback linearizable nonlinear systems possessing unknown nonlinearities, capable of guaranteeing a prescribed performance, is developed in this paper. By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. Visualizing the prescribed performance characteristics as tracking error constraints, the key idea is to transform the ldquoconstrainedrdquo system into an equivalent ldquounconstrainedrdquo one, via an appropriately defined output error transformation. It is shown that stabilization of the ldquounconstrainedrdquo system is sufficient to solve the stated problem. Besides guaranteeing a uniform ultimate boundedness property for the transformed output error and the uniform boundedness for all other signals in the closed loop, the proposed robust adaptive controller is smooth with easily selected parameter values and successfully bypasses the loss of controllability issue. Simulation results on a two-link robot, clarify and verify the approach.

Adaptive Control with Recurrent High-order Neural Networks

1. Introduction.- 1.1 General Overview.- 1.2 Book Goals & Outline.- 1.3 Notation.- 2. Identification of Dynamical Systems Using Recurrent High-order Neural Networks.- 2.1 The RHONN Model.- 2.1.1 Approximation Properties.- 2.2 Learning Algorithms.- 2.2.1 Filtered Regressor RHONN.- 2.2.2 Filtered Error RHONN.- 2.3 Robust Learning Algorithms.- 2.4 Simulation Results.- Summary.- 3. Indirect Adaptive Control.- 3.1 Identification.- 3.1.1 Robustness of the RHONN Identifier Owing to Unmodeled Dynamics.- 3.2 Indirect Control.- 3.2.1 Parametric Uncertainty.- 3.2.2 Parametric plus Dynamic Uncertainties.- 3.3 Test Case: Speed Control of DC Motors.- 3.3.1 The Algorithm.- 3.3.2 Simulation Results.- Summary.- 4. Direct Adaptive Control.- 4.1 Adaptive Regulation - Complete Matching.- 4.2 Robustness Analysis.- 4.2.1 Modeling Error Effects.- 4.2.2 Model Order Problems.- 4.2.3 Simulations.- 4.3 Modeling Errors with Unknown Coefficients.- 4.3.1 Complete Model Matching at |x| = 0.- 4.3.2 Simulation Results.- 4.4 Tracking Problems.- 4.4.1 Complete Matching Case.- 4.4.2 Modeling Error Effects.- 4.5 Extension to General Affine Systems.- 4.5.1 Adaptive Regulation.- 4.5.2 Disturbance Effects.- 4.5.3 Simulation Results.- Summary.- 5. Manufacturing Systems Scheduling.- 5.1 Problem Formulation.- 5.1.1 Continuous Control Input Definition.- 5.1.2 The Manufacturing Cell Dynamic Model.- 5.2 Continuous-time Control Law.- 5.2.1 The Ideal Case.- 5.2.2 The Modeling Error Case.- 5.3 Real-time Scheduling.- 5.3.1 Determining the Actual Discrete Dispatching Decision.- 5.3.2 Discretization Effects.- 5.4 Simulation Results.- Summary.- 6. Scheduling using RHONNs: A Test Case.- 6.1 Test Case Description.- 6.1.1 General Description.- 6.1.2 Production Planning & Layout in SHW.- 6.1.3 Problem Definition.- 6.1.4 Manufacturing Cell Topology.- 6.1.5 RHONN Model Derivation.- 6.1.6 Other Scheduling Policies.- 6.2 Results & Comparisons.- Summary.- References.

Prescribed Performance Adaptive Control for Multi-Input Multi-Output Affine in the Control Nonlinear Systems

We consider the tracking problem of unknown, robustly stabilizable, multi-input multi-output (MIMO), affine in the control, nonlinear systems with guaranteed prescribed performance. By prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants. Utilizing an output error transformation, we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system, provided that initially the transformed system is well defined. Consequently, a switching robust control Lyapunov function (RCLF)-based adaptive, state feedback controller is designed, to solve the stated problem. The proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable. Simulations illustrate the approach.

Direct adaptive regulation of unknown nonlinear dynamical systems via dynamic neural networks

A direct nonlinear adaptive state regulator, for unknown dynamical systems that are modeled by dynamic neural networks is discussed. In the ideal case of complete model matching, convergence of the state to zero plus boundedness of all signals in the closed loop is ensured. Moreover, the behavior of the closed loop system is analyzed for cases in which the true plant differs from the dynamic neural network model in the sence that it is of higher order, or due to the presence of a modeling error term. In both cases, modifications of the original control and update laws are provided, so that at least uniform ultimate boundedness is guaranteed, even though in some cases the stability results obtained for the ideal case are retained.

A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems

Abstract A universal, approximation-free state feedback control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed performance and bounded closed loop signals. By prescribed performance, it is meant that the output error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, having maximum overshoot less than a preassigned level. The proposed state feedback controller isolates the aforementioned output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties, while completely avoiding the explosion of complexity issue raised by backstepping-like approaches that are typically employed to the control of pure feedback systems. In this respect, a low complexity design is achieved. Moreover, the controllability assumptions reported in the relevant literature are further relaxed, thus enlarging the class of pure feedback systems that can be considered. Finally, simulation studies clarify and verify the approach.

Robust Partial-State Feedback Prescribed Performance Control of Cascade Systems With Unknown Nonlinearities

A universal controller is designed for cascade systems, involving dynamic uncertainty, unknown nonlinearities, exogenous disturbances and/or time-varying parameters, capable of guaranteeing prescribed performance for the output tracking error, as well as uniformly bounded signals in the closed loop. By prescribed performance we mean that the output tracking error should converge to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, exhibiting maximum overshoot less than a sufficiently small preassigned constant. The proposed control scheme is of low complexity, utilizes partial state feedback and requires reduced levels of a priori system knowledge. The results can be easily extended to systems affected by bounded state measurement errors, as well as to MIMO nonlinear systems in block triangular form. Simulations clarify and verify the approach.

Adaptive Dynamic Output Feedback Neural Network Control of Uncertain MIMO Nonlinear Systems With Prescribed Performance

An adaptive dynamic output feedback neural network controller for a class of multi-input/multi-output affine in the control uncertain nonlinear systems is designed, capable of guaranteeing prescribed performance bounds on the systems output as well as boundedness of all other closed loop signals. It is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration. The proposed dynamic controller is of switching type. However, its continuity is guaranteed, thus alleviating any issues related to the existence and uniqueness of solutions. Simulations on a planar two-link articulated manipulator illustrate the approach.

Stable adaptive neuro-control design via Lyapunov function derivative estimation

A new approach to the tracking problem, for affine in the control nonlinear dynamical systems, whose nonlinearities are assumed to be unknown, is presented in this paper. The philosophy of the developed technique is based on estimating the derivative of an unknown Lyapunov function, exploiting the approximation capabilities of the linear in the weights neural network structures. A novel resetting strategy guarantees the boundedness away from zero of certain signals. The uniform ultimate boundedness of the tracking error to an arbitrarily small set, plus the boundedness of all other signals in the closed loop is guaranteed.

Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity

In this paper, we consider the design of tracking controllers for flexible joint robots with unknown and possibly variable elasticity, achieving pre-set performance attributes on the link position error. The developed full state feedback controller, is realized without incorporating knowledge relative to the actual system nonlinearities. Furthermore, no approximators are employed to acquire such information. Comparative simulation results on a 2-d.o.f. flexible joint manipulator, illustrate the efficiency of the approach.

Brief paper: Force/position tracking for a robotic manipulator in compliant contact with a surface using neuro-adaptive control

The problem of force/position tracking for a robotic manipulator in compliant contact with a surface under non-parametric uncertainties is considered. In particular, structural uncertainties are assumed to characterize the compliance and surface friction models, as well as the robot dynamic model. A novel neuro-adaptive controller is proposed, that exploits the approximation capabilities of the linear in the weights neural networks, guaranteeing the uniform ultimate boundedness of force and position error with respect to arbitrarily small sets, plus the boundedness of all signals in the closed loop. Simulations highlight the approach.