From Adaptive Differential Games to Disturbance-Robust Adaptive Control

Many dynamic systems containing a large number of modes can benefit from adaptive control techniques, which are well suited to applications that have unknown parameters and poorly known operating conditions. In this paper, we focus on a model reference direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend this adaptive control theory to accommodate problematic modal subsystems of a plant that inhibit the adaptive controller by causing the open-loop plant to be non-minimum phase. We will augment the adaptive controller using a Residual Mode Filter (RMF) to compensate for problematic modal subsystems, thereby allowing the system to satisfy the requirements for the adaptive controller to have guaranteed convergence and bounded gains. We apply these theoretical results to design an adaptive collective pitch controller for a high-fidelity simulation of a utility-scale, variable-speed wind turbine that has minimum phase zeros.

This paper investigates a single parameter adaptive neural network control method for unknown nonlinear systems with bounded external disturbances. A smooth performance function is developed to achieve the transient and steady state of system tracking error that could be constrained in prescribed bounds. The difficulties in dealing with unknown system parameters and disturbances of nonlinear systems are resolved based on the single parameter adaptive neural network control which is proposed to effectively reduce the calculation amount. The theoretical analysis implies that the proposed control scheme makes the closed‐loop system uniformly ultimately bounded. Simulation demonstrates that the proposed adaptive controller gives a favorable performance on tracking desired signal and constraining the bounds of tracking error which could be arbitrarily small with appropriate adaptive parameters. Both the theoretical analysis and simulations confirm the effectiveness of the control scheme.

In conventional immersion and invariance (I&I) adaptive control design, control parameter adaptation is typically linear with respect to the parameter error-induced perturbation, resulting in quadratic rate dissipation of energy associated with the off-the-manifold variable. Departing from such a convention, this article contributes a novel strategy—polynomial adaptation. As the name suggests, control parameter adaptation in this approach takes the form of a general polynomial in relation to the perturbation. Accordingly, this new design induces polynomial rate energy dissipation, which is faster than the quadratic one in the conventional scheme, thereby enhancing closed-loop control performance. The theoretical underpinnings of the new approach are demonstrated through the design of an I&I adaptive tracking control law for a general nth-order, single-input–single-output, parametrically uncertain, nonlinear system in the controllable canonical form. In addition, a numerical study of the proposed method on the second-order forced Duffing oscillator shows its improved transient performance in comparison to a baseline controller developed with the standard I&I adaptive control technique.

In this paper, a nonlinear adaptive robust control method is presented for a single-rod electro-hydraulic actuator with unknown nonlinear parameters. Previous adaptive control methods of hydraulic systems always assume that the system's unknown parameters occur linearly, but, in a practical hydraulic system, unknown nonlinear parameters, which enter the system equations in a nonlinear way, are common; for example, when the original control volumes are unknown or change, uncertain nonlinear parameters will exist. The proposed control method in this paper is to present a nonlinear adaptive controller with adaptation laws to compensate for the uncertain nonlinear parameters due to the varieties of the original control volumes. The main feature of the scheme is that a novel-type Lyapunov function is developed to construct an asymptotically stable adaptive controller and adaptation laws. Furthermore, by combining backstepping techniques and a simple robust control method, the whole system's controller and adaptation laws are presented, which can compensate for all unknown parameters and uncertain nonlinearities. The experimental results show that the nonlinear control algorithm, together with the adaptation scheme, gives a good performance for the specified tracking task in the presence of unknown nonlinear parameters.

Air-to-air missile guidance laws are derived using optimal control and differential game theory with final miss distance as the optimization criterion. A perfect target airframe/autopilot response is assumed, while both perfect and first-order missile responses are considered. With a first-order missile response the target is always able to force a nonzero final miss distance in the differential game formulation. For all other formulations considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e.g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors in estimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario; whereas for the inner launch boundary scenario the laws based on a first-order missile response achieved smaller miss distances.

In contrast, the differential game approach Air-to-air missile guidance laws are derived makes no assumption on future target maneuvers, using optimal control and differential game theory but instead takes into consideration the target's with final miss distance as the optimization cri- maneuver capabilities. The guidance law then terion. A perfect target airframe /autopilot re - guides the missile so as to minimize the potential sponse is assumed, while both perfect and first effects of the target's intelligent use of hie maorder missile responses are considered. With a neuver capabilities. first order missile response the target is always able to force a non zero final miss distance in the differential game formulation. For all other formulaticjns considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e. g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors i,: rstimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario, whereas for the inner launch boundary scenario the laws based on a first order missile response achieved srnaller miss distances. The purpose of this paper

This paper addresses the adaptive position tracking control problem for high-speed trains with time-varying resistances and mass in the motion dynamics. To handel these time-varying parameters with piecewise constant characteristics, a piecewise constant model with unknown parameters is introduced for different train operation conditions. An integrated adaptive controller structure is constructed to have the capacity to achieve plant-model matching with known parameters and complete system parametrization with unknown parameters, which is desirable for adaptive tracking control. For the train position tracking requirement, the reference model system is specifically chosen. Stable adaptive laws are designed to update the adaptive controller parameters in the presence of the unknown piecewise constant system parameters. Closed-loop stability and asymptotic state tracking are proved. Simulation results on a high-speed train model are presented to illustrate the desired adaptive position tracking control performance.

We have previously shown that region 2 energy capture can be increased by using adaptive torque gain control on variable speed turbines. This adaptive torque control works by compensating for unknown and time-varying aerodynamic parameters such as the maximum power coefficient Cpmax and its corresponding optimal tip speed ratio λ*. This paper extends our earlier research in two ways in order to make the adaptive control technique more appealing to the commercial wind turbine industry. These two extensions are the use of the nacelle anemometer and the extension to a second-order discrete filter in the gain adaptation law. We believe that these two extensions will allow the adaptive controller to achieve its increased energy capture at lower cost and less sensitivity to noise than was possible with our original adaptive control strategy.

This book gives an exposition of recently developed approximate dynamic programming (ADP) techniques for decision and control in human engineered systems. ADP is a reinforcement machine learning technique that is motivated by learning mechanisms in biological and animal systems. It is connected from a theoretical point of view with both adaptive control and optimal control methods. The book shows how ADP can be used to design a family of adaptive optimal control algorithms that converge in real-time to optimal control solutions by measuring data along the system trajectories. Generally, in the current literature adaptive controllers and optimal controllers are two distinct methods for the design of automatic control systems. Traditional adaptive controllers learn online in real time how to control systems, but do not yield optimal performance. On the other hand, traditional optimal controllers must be designed offline using full knowledge of the systems dynamics. It is also shown how to use ADP methods to solve multi-player differential games online. Differential games have been shown to be important in H-infinity robust control for disturbance rejection, and in coordinating activities among multiple agents in networked teams. The focus of this book is on continuous-time systems, whose dynamical models can be derived directly from physical principles based on Hamiltonian or Lagrangian dynamics.

Most of the literature on oligopoly deals with profit-maximizing firms engaging in “static” repetitive games. As the number of firms increases, the Nash-equilibrium strategy for each Cournot oligopolist converges to the competitive solution. In a two-person, zero-sum differential game model of duopoly [1] we introduced dynamic elements and explored alternative entrepreneurial goals. The duopolists endeavor to outsell each other subject to a no-loss constraint; the saturation of present markets by past sales and the impact on future goodwill by current advertisement are handled through “state variables.” The differential game formulation [1, 2] offers two advantages: (a) near perfect information leads to frequent existence of pure strategy equilibria and (b) the use of optimal control theory facilitates the characterization of the time structure of an equilibrium. However, the two-person, zero-sum framework is too restrictive while a general theory for solving n-person, non-zero sum differential games has still not been developed [3, 4].

This paper studies the real-time parameter estimation and adaptive tracking control problem for a six degrees of freedom (6-DOF) of quadrotor unmanned aerial vehicle (UAV) as an under-actuated system. A virtual proportional derivative (PD) is proposed to maintain position dynamics. Two adaptive control schemes are designed and compared to maintain the attitude dynamics of UAV while several parameters of UAV are unknown. In the first scheme, a classical adaptive scheme using the certainty equivalence principle is extended and designed for tracing control of the systems with unknown time-varying parameters. To improve the performance of the first scheme, a new control scheme is designed in the second scheme by proposing additional continuous function to handle the unknown parameters. An additional robust term is designed in both schemes to handle the perturbation caused by unknown time-varying parameters. The rigorous analytical proof and numerical simulation analysis are provided to support the efficacy of the proposed controller.

The accurate modeling of wind turbines is an extremely challenging problem due to the tremendous complexity of the machines and the turbulent and unpredictable conditions in which they operate. Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. In this paper, we extended the direct model reference adaptive control (DMRAC) approach to track a reference point and to reject persistent disturbances. This approach was then used to design an adaptive collective pitch controller for a high‐fidelity simulation of a variable‐speed horizontal axis wind turbine. The objective of the adaptive pitch controller was to regulate generator speed in Region 3 and to reject step disturbances. The control objective was accomplished by collectively pitching the turbine blades.The turbine simulation models the controls advanced research turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility‐scale wind turbine that has a well‐developed and extensively verified simulator. This novel application of adaptive control was compared in simulations with a classical proportional integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the PI pitch controller. Copyright © 2008 John Wiley & Sons, Ltd.

From adaptive control to variable structure systems – seeking harmony

Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. The turbulent and unpredictable conditions in which wind turbines operate create many challenges for their operation. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility scale, variable-speed horizontal axis wind turbine. The objective of the adaptive pitch controller in Region 3 is to regulate generator speed and reject step disturbances. The control objective is accomplished by collectively pitching the turbine blades. We use an extension of the Direct Model Reference Adaptive Control (DMRAC) approach to track a reference point and to reject persistent disturbances. The turbine simulation models the Controls Advanced Research Turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility-scale wind turbine which has a well-developed and extensively verified simulator. The adaptive collective pitch controller for Region 3 was compared in simulations with a bas celliansesical Proportional Integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the baseline PI pitch controller and it demonstrated robustness to modeling errors.

Adaptive quantile control for stochastic system