Certainty Equivalence Control Law Research Articles

Sampled-Data Cooperative Output Regulation: An Adaptive Distributed Continuous-Discrete Observer Approach

This paper studies the sampled-data cooperative output regulation problem for linear multi-agent systems. Firstly, a novel adaptive distributed continuous-discrete observer is established to recover the leader's state, which, on one hand, only relies on the sampling output of the leader, and on the other hand, does not need to store the sampled message from neighbors. Secondly, by solely making use of the digital states of both the agent and the distributed observer, a certainty equivalence control law is synthesized featuring a time-varying feedforward gain. It is rigorously proven that, with this time-varying feedforward gain, the proposed control approach can achieve exponential convergence of the tracking errors given arbitrary time-varying leader's signal, and the upper bound for the sampling intervals is explicitly given. Thirdly, for the class of chain-integrator multi-agent systems, the proposed control approach does not need any restriction on the upper bound of the sampling intervals, and thus would be more practical in certain application scenarios from the perspective of energy saving. The performance of the proposed control approach is validated by the simulation results of inverter-based distributed generation systems.

Power Tracking and Energy Balancing of Energy Storage Systems under Unreliable Communication Network

In this paper, we consider the distributed power tracking and energy balancing problem of a general energy storage system subject to unreliable switching communication network. In order to deal with the uncertainty of the network topology, a distributed observer-based approach has been proposed. First, an adaptive distributed observer is employed to recover the reference power for the entire energy storage system for each energy storage unit. Second, based on the estimated reference power, a certainty equivalent control law is synthesized to simultaneously achieve power tracking and energy balancing. Numerical simulations are provided to validate the proposed control approach.

Adaptive fuzzy PD control with stable H∞ tracking guarantee

For indirect adaptive fuzzy H∞ tracking control (AFHC) of perturbed uncertain nonlinear systems, sliding-mode control (SMC) compensation usually has to be applied to ensure stability and H∞ robustness of the closed-loop system. We prove that indirect AFHC without SMC compensation is sufficient to guarantee stable H∞ tracking under given initial conditions and parameter constraints. The control structure only includes an indirect adaptive fuzzy control term and a proportional derivative (PD) control term. A certainty equivalent control law is slightly modified such that both a lumped perturbation and adaptive laws are independent of the PD control term. This modification is significant since it not only plays a key role in stability analysis, but also alleviates some drawbacks of existing AFHC approaches for practical applications. An illustrative example has been provided to verify correctness of the theoretical result.

Wing rock control by finite-form adaptation

The wing rock (self-excited rolling motion) of aircraft flying at high angle of attack adversely affects the handling qualities and maneuverability. This paper presents new adaptation algorithms in finite (integral-algebraic) form for the wing rock control. The objective is to stabilize the rolling motion, despite parameter uncertainties. Two adaptive control laws in finite form are derived for the trajectory control of the roll angle. The first control system is obtained by the realization of a speed-gradient adaptation law, and an immersion and invariance-based adaptive law is used for the second controller. Unlike the certainty-equivalent control laws, these adaptation laws include an integral term as well as a judiciously chosen nonlinear algebraic vector function. The algebraic function in the adaptation law provides stronger stability properties in the closed-loop system. Simulation results show that the designed adaptive controllers are capable of suppressing the wing rock motion of the model, despite uncertainties in the parameters.

Noncertainty-Equivalent Adaptive Wing-Rock Control via Chebyshev Neural Network

Aircraft flying at high angles of attack exhibit self-excited rolling motion (termed wing rock). This paper presents a noncertainty-equivalent adaptive control system for the wing-rock motion control via a Chebyshev neural network. The unmodeled nonlinearity of the system is approximated by a Chebyshev neural network using polynomials in roll angle and roll rate of the first kind. An adaptive control law is derived for the trajectory control of the roll angle. The control system includes a control module and a parameter identifier and uses filtered signals for synthesis. Unlike the certainty-equivalent control laws, each estimated parameter is the sum of a judiciously chosen nonlinear function and a partial estimate generated by an integral adaptation law. The nonlinear function in the parameter estimate provides stronger stability property in the closed-loop system. Simulation results are presented that show that the adaptive Chebyshev neural controller is capable of suppressing the wing-rock motion of the model with unknown nonlinearity and disturbance input at different angles of attack.

Immersion- and Invariance-Based Adaptive Control ofa Nonlinear Aeroelastic System

This paper treats the question of adaptive control of prototypical aeroelastic wing sections with structural nonlinearity based on the immersion and invariance approach. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. A single control surface is used for the purpose of control. It is assumed that the model parameters except the sign of coefficient of control input are unknown. A noncertaintyequivalent adaptive control law for the trajectory tracking of the pitch angle is derived. Using Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. Unlike the certainty-equivalent control laws developed in literature for aeroelastic systems, this new control system can accomplish superior tracking performance. A special feature of the designed control system is that, whenever the estimated parameters coincide with their true values, the adaptation stops and the closed-loop system recovers the performance of deterministic closed-loop system. This cannot happen if certainty-equivalent adaptive controllers are used. Furthermore, the trajectory of the closed-loop system, including the noncertainty-equivalent adaptive law, is eventually confined to a manifold in the space of state variables and parameter estimates. Simulation results using the new controller and the conventional certainty-equivalent controller are presented. These results show that the new controller performs better in suppressing oscillatory responses of the wing in the presence of large parameter uncertainties.

Stochastic Linear Control Over a Communication Channel

We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular, we examine the role communication has on the classical linear quadratic Gaussian problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeoffs between control and communication costs. In particular, we show that optimal quadratic cost decomposes into two terms: A full knowledge cost and a sequential rate distortion cost.

Almost Optimal Adaptive LQ Control: SISO Case

In this paper an almost optimal indirect adaptive controller for input/output dynamical systems is proposed. The control part of the adaptive control scheme is based on a modified LQ control law: by adding a time-varying gain to the certainty equivalent control law the conflict between identification and control is avoided.

Discrete-time entropy formulation of optimal and adaptive control problems

The discrete-time version of the entropy formulation of optimal control of problems developed by G.N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws. >

Stable Indirect Adaptive Control of Continuous-Time Systems with No A Priori Knowledge on the Parameters

Abstract A crucial drawback of indirect adaptive control is the stabilizability or controllability of the estimated plant model which is required in order to calculate the controller parameters. Loss of stabilizability at a particular instant of time may lead to unbounded signais. In this paper, we propose an indirect adaptive control scheme that overcomes the stabilizability problem, and meets the control objective exactly with no additional a priori knowledge on the unknown plant other than its order. The control scheme switches from the usual certainty equivalence control law to a rich open loop control input, according to an adjustable lower bound for the degree of stabilizability of the estimated plant model. The switching terminates in finite time after which no loss of stabilizability can occur, and the certainty equivalence control law is on for the rest of the: me. In contrast to previous schemes, the proposed scheme, referred to as the switched-excitation approach, requires no knowledge of bounds for the stabilizability degree of the unknown plant and guarantees closed-loop stability and zero residual tracking error.

Modified algorithm for MIMO self-tuning control

Abstract A modified certainty-equivalent algorithm for multi-input multi-output (MIMO) self-tuning control is proposed in this paper. The main feature of the algorithm is that the certainty-equivalent control law within the self-tuning structure is modified to improve its effectiveness. A simulation example is used to illustrate the algorithm.

The certainty equivalence property in stochastic control theory

In this paper we will give a general formulation of the certainty equivalence principle for stochastic optimal control problems. Special attention is paid to the question: What do we mean by a certainty equivalence control law? It is then shown that in this context the LQG-problem is indeed certainty equivalent.

Estimation and control performance for space-time point-process observations

Estimation and control problems are examined for a class of models involving a linear system, a quadratic cost, and observations that include a space-time point as well as the familiar signal in additive Wiener process measurements. Motivation for this class of models is given in terms of position sensing and tracking for quantum-limited optical communication problems. These models include as special eases several simpler ones considered previously. As in the simpler cases, the optimum estimator is finite-dimensional and nonlinear, and the optimum controller separates into the optimum estimator followed by the certainty-equivalent control law. Although the optimum estimator and the optimum controller are finite-dimensional, the corresponding expected error covariance and optimum cost require infinite-dimensional calculations. This motivates the derivation of easily-computed upper and lower bounds on estimator and controller performance. The upper bounds are derived by evaluating exactly the performance of a parametrized family of suboptimum designs; one of these is identified as having smaller performance than any other, thus providing a minimal upper bound within this family. The lower bounds are obtained directly by calculations involving inequalities.