Control Of Uncertain Dynamical Systems Research Articles

Robust adaptive control of uncertain dynamic systems using self-evolving neural learning technique

Robust adaptive control of uncertain dynamic systems using self-evolving neural learning technique

UKF-Based Optimal Tracking Control for Uncertain Dynamic Systems With Asymmetric Input Constraints.

To enhance system robustness in the face of uncertainty and achieve adaptive optimization of control strategies, a novel algorithm based on the unscented Kalman filter (UKF) is developed. This algorithm addresses the finite-horizon optimal tracking control problem (FHOTCP) for nonlinear discrete-time (DT) systems with uncertainty and asymmetric input constraints. An augmented system is constructed with asymmetric control constraints being considered. The augmented problem is addressed with a DT Hamilton-Jacobi-Bellman equation (DTHJBE). By analyzing convergence with regard to the cost function and control law, the UKF-based iterative adaptive dynamic programming (ADP) algorithm is proposed. This algorithm approximates the solution of the DTHJBE, ensuring that the cost function converges to its optimal value within a bounded range. To execute the UKF-based iterative ADP algorithm, the actor-estimator-critic framework is built, in which the estimator refers to system state estimation through the application of UKF. Ultimately, simulation examples are presented to show the performance of the proposed method.

Structured Learning of Safety Guarantees for the Control of Uncertain Dynamical Systems

Approaches to keeping a dynamical system within state constraints typically rely on a model-based safety condition to limit the control signals. In the face of significant modeling uncertainty, the system can suffer from important performance penalties due to the safety condition becoming overly conservative. Machine learning can be employed to reduce the uncertainty around the system dynamics, and allow for higher performance. In this article, we propose the safe uncertainty-learning principle, and argue that the learning must be properly structured to preserve safety guarantees. For instance, robust safety conditions are necessary, and they must be initialized with conservative uncertainty bounds prior to learning. Also, the uncertainty bounds should only be tightened if the collected data sufficiently captures the future system behavior. To support the principle, two example problems are solved with control barrier functions: a lane-change controller for an autonomous vehicle, and an adaptive cruise controller. This work offers a way to evaluate whether machine learning preserves safety guarantees during the control of uncertain dynamical systems. It also highlights challenging aspects of learning for control.

High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.

Safe Learning for Control using Control Lyapunov Functions and Control Barrier Functions: A Review

Real-world autonomous systems are often controlled using conventional model-based control methods. But if accurate models of a system are not available, these methods may be unsuitable. For many safety-critical systems, such as robotic systems, a model of the system and a control strategy may be learned using data. When applying learning to safety-critical systems, guaranteeing safety during learning as well as testing/deployment is paramount. A variety of different approaches for ensuring safety exists, but the published works are cluttered and there are few reviews that compare the latest approaches. This paper reviews two promising approaches on guaranteeing safety for learning-based robust control of uncertain dynamical systems, which are based on control barrier functions and control Lyapunov functions. While control barrier functions provide an option to incorporate safety in terms of constraint satisfaction, control Lyapunov functions are used to define safety in terms of stability. This review categorises learning-based methods that use control barrier functions and control Lyapunov functions into three groups, namely reinforcement learning, online and offline supervised learning. Finally, the paper presents a discussion of the suitability of the different methods for different applications.

Cooperative Game Approach to Robust Control Design for Fuzzy Dynamical Systems.

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

Adaptive control for uncertain dynamical systems with nonlinear reference systems

ABSTRACTA reference model of an adaptive control law defines how a closed-loop dynamical system under consideration has to asymptotically (or approximately) behave in the presence of system uncertainties. While it is of common practice to use reference models with linear dynamics, this can lead to limitations on the achievable closed-loop dynamical system performance – especially for applications involving highly capable dynamical systems such as highly manoeuvrable aircraft, missiles, and space launch vehicles. Because, linear reference models for these applications can only approximate the desired closed-loop behaviour of these nonlinear dynamical systems in narrow regions of the state-space. Motivated from this standpoint, this paper's contribution is to present a new adaptive control architecture for uncertain dynamical systems based on nonlinear reference models. Specifically, we analytically show that the system error between the uncertain dynamical system and the nonlinear reference model asymptotically vanishes in steady-state and its performance is guaranteed during the transient-time. We further discuss the practicality of our approach and provide numerical examples to demonstrate its efficacy.

Multi-Kernel Online Reinforcement Learning for Path Tracking Control of Intelligent Vehicles

Path tracking control of intelligent vehicles has to deal with the difficulties of model uncertainties and nonlinearities. As a class of adaptive optimal control methods, reinforcement learning (RL) has received increasing attention in solving difficult control problems. However, feature representation and online learning ability are two major problems to be solved for learning control of uncertain dynamic systems. In this article, we propose a multi-kernel online RL approach for path tracking control of intelligent vehicles. In the proposed approach, a multiple kernel feature learning framework is designed for online learning control based on dual heuristic programming (DHP) and the new online learning control algorithm is called multi-kernel DHP (MKDHP). In MKDHP, instead of the expert knowledge for selecting and fine-tuning of a suitable kernel function, only a set of basic kernel functions is required to be predefined and the multi-kernel features can be learned for value function approximation in the critic. The simulation studies on path tracking control for intelligent vehicles have been conducted under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -curve and urban road conditions. The results demonstrated that compared with other typical path tracking controllers for intelligent vehicles, such as the linear quadratic regulator (LQR), the pure pursuit controller and the ribbon-based controller, the proposed multi-kernel learning controller can achieve better performance in terms of tracking precision and smoothness.

Fuzzy dynamical system approach for a dual-parameter hybrid-order robust control design

Robust control for uncertain dynamical systems is considered. The uncertainty is assumed to be bounded, and the fuzzy set theory is adopted to describe the bound. A new dual-parameter hybrid-order robust control design is then proposed in two steps. First, a class of robust controls is designed, taking the advantage of the flexibility in choosing the order and a design parameter. The controls are deterministic and are not IF–THEN fuzzy rules-based. Deterministic performance, including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed. Second, a fuzzy-set theoretic based performance index consisting of average and steady state system performance and control cost is proposed. A constrained optimization problem is formulated with the intension of minimizing the performance index. The objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index. We show that the solution to the optimization problem always exists. As a result, the resulting control design achieves two concurrent goals: guaranteeing deterministic performance as well as minimizing the performance index. The theory is illustrated by an unmanned aerial vehicle (UAV) system control design.

Rendering Optimal Design in Controlling Fuzzy Dynamical Systems: A Cooperative Game Approach

This study investigates the robust control for uncertain dynamical systems. The uncertainty is (possibly fast) time-varying but bounded. We adopt the fuzzy set theory to describe the uncertainty in the system (hence, called the fuzzy dynamical system). A class of robust controls is proposed based on tunable parameters. The controls are deterministic and are not conventional IF–THEN fuzzy rules based (such as Mamdani type). The proposed controls are able to guarantee deterministic system performance, namely uniform boundedness and uniform ultimate boundedness. In the phase of searching for the optima from the pool of admissible control design parameters, we formulate this as a two-player cooperative game by developing two performance indexes (i.e., the cost functions), each of which is dominated by one tunable parameter (i.e., the player). By the cooperative game theory, we are able to obtain the Pareto-optimality (i.e., the optima of tunable parameters). Simulation results on an electric vehicle motion control problem are presented for demonstration.

A command governor approach to set-theoretic model reference adaptive control for enforcing partially adjustable performance guarantees

In feedback control, the presence of system uncertainties cause system state trajectories to deviate from their ideal responses. In practice, a subset of these trajectories can be more critical than the rest due to physical and/or performance characteristics associated with a problem of interest. Hence, it is desired not only to have performance guarantees on the entire system state trajectories but also to be able to adjust the resulting worst-case performance bound for that critical subset. Yet, in model reference adaptive control of uncertain dynamical systems, assigning performance bounds on a subset of system trajectories is not trivial. This paper addresses this gap by proposing a new control architecture that has the capability to enforce a user-defined performance bound on the selected subset of dynamical system trajectories, entitled as partially adjustable performance guarantees. The proposed architecture is predicated on a set-theoretic treatment and utilizes a two-level constructive design framework. In particular, we first form an auxiliary state dynamics in order to construct the auxiliary system error vector between uncertain dynamical system states and this auxiliary dynamics states. This construction aids a control designer to weigh each element of the auxiliary system error vector independently, while enforcing performance bounds on the norm of this error vector. Then, a command governor mechanism is designed for driving a feasible user-selected subset of system states to a close (and user-controllable) neighborhood of the corresponding reference model states. This results in adjustable performance guarantees on a subset of system error trajectories.

A fuzzy fractional-order control of robotic manipulators with PID error manifolds

The present paper proposes a model-free implementation and output feedback control for robust tracking of robotic manipulators. By considering the salient advantages of fuzzy logic techniques for the control of uncertain dynamic systems, as well as the intrinsic properties of fractional-order (FO) operators for modelling and control of complex engineering processes, this paper proposes a control scheme that relies on fuzzy logic and FO tools. Firstly, a proportional–integral–derivative (PID) error manifold is synthesised to enhance the tracking capabilities of the closed-loop system. Then, in order to guarantee that the PID extended error evolves close to the origin, the dynamic controller is build upon a Takagi–Sugeno inference system, which is based on the PID extended error and on its FO integral. Finally, the reliability of the proposed method is demonstrated by means of a numerical simulation, and comparisons are carried out in experiments versus trustworthy discontinuous and continuous sliding mode based controllers.

Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

SummaryIn adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.

A neuroadaptive architecture for model reference control of uncertain dynamical systems with performance guarantees

Neuroadaptive control systems have the capability to approximate unstructured system uncertainties on a given compact set using neural networks. Yet, a challenge in their design is to guarantee the closed-loop system trajectories stay in this set such that the universal function approximation property is satisfied and the overall system stability is achieved. To address this challenge, we present and analyze a new neuroadaptive architecture in this paper for model reference control of uncertain dynamical systems with strict performance guarantees. Specifically, the proposed architecture is predicated on a novel set-theoretic framework and has the capability to keep the closed-loop system trajectories within an a-priori, user-defined compact set without violating the universal function approximation property. A transport aircraft example is also given to complement the presented theoretical results.

Active disturbance rejection control: Applications in aerospace

Control of uncertain dynamical systems has been an area of active research for the past several decades and to this end, various robust control approaches have been proposed in the literature. The active disturbance rejection control (ADRC) represents one prominent approach that has been widely studied and applied for designing robust controllers in diverse areas of engineering applications. In this work, a brief review of the approach and some of its applications in aerospace are discussed. The results show that the approach possesses immense potential to offer viable solution to real-life aerospace problems.

Persistence in Control Systems

In this letter, we propose concepts of persistence and persistent control for uncertain dynamical systems. Motivated from their application to local controller design for expanding huge-scale systems, a problem of persistent control is formulated. A controller is designed such that for any arbitrarily large uncertainty the overall control system is stable. In addition, the performance of the overall system, measured by some norm, can be deteriorated for the large uncertainty, but is persistently prevented from being collapsed. Then, the control problem is solved via controller parametrization, and the characterization of the persistent controllers is given. Finally, a numerical example with some design guideline of the controller is illustrated.

An Adaptive Architecture for Control of Uncertain Dynamical Systems with Unknown Actuator Bandwidths

Closed-loop system stability of adaptive control architectures for autonomous aerospace vehicles can be seriously degraded by the presence of actuator dynamics. To this end, recent research by the authors focuses on a new reference model design approach such that not only closed-loop system stability is rigorously addressed using linear matrix inequalities, but also the proposed reference model achieves better performance characteristics as compared with a well-adopted method in the literature called pseudo-control hedging. Yet, this reference model assumes the exact knowledge of the actuator bandwidth parameter, where such an assumption may not always hold for practical aerospace applications. Motivated from this standpoint, this paper generalizes our recent results such that the exact knowledge of the actuator bandwidth parameter is no longer necessary. Specifically, we utilize an online estimate of the actuator bandwidth parameter in the proposed reference model and show the stability of the closed-loop dynamical system using tools and methods from Lyapunov theory and linear matrix inequalities. An illustrative numerical example involving the short-period dynamics of a hypersonic vehicle model is also included in this paper to elucidate the proposed adaptive architecture for control of uncertain dynamical systems with unknown actuator bandwidths.

Optimal control of uncertain systems with jump under optimistic value criterion

Based on uncertainty theory, a new optimistic value model of uncertain optimal control for uncertain dynamic systems with jump is established. The principle of optimality is proposed and the equation of optimality is obtained for presented model by employing the dynamic programming method. As an application, an optimal control problem of pension fund is discussed to verify the validity of the proposed method.

Computing actuator bandwidth limits for model reference adaptive control

ABSTRACTAlthough model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Reliable Dissipative Sampled-Data Control for Uncertain Systems With Nonlinear Fault Input

This paper investigates the robust reliable β-dissipative control for uncertain dynamical systems with mixed actuator faults via sampled-data approach. In particular, a more general reliable controller containing both linear and nonlinear parts is constructed for the considered system. Then, by applying the input delay approach, the sampling measurement of the digital control signal is transformed into time-varying delayed one. The aim of this paper is to design state feedback sampled-data controller to guarantee that the resulting closed-loop system to be strictly (Q, S, R)-β-dissipative. By constructing appropriate Lyapunov function and employing a delay decomposition approach, a new set of delay-dependent sufficient stabilization criteria is obtained in terms of linear matrix inequalities (LMIs). Moreover, the obtained LMIs are dependent, not only upon upper bound of time delay but also depend on the dissipative margin β and the actuator fault matrix. As special cases, H∞ and passivity control performances can be deduced from the proposed dissipative control result. Finally, numerical simulation is provided based on a flight control model to verify the effectiveness and applicability of the proposed control scheme.