Distributed Composite Adaptive Synchronization of Multiple Uncertain Euler-Lagrange Systems using Cooperative Initial Excitation

Combined Cooperative Adaptive Cruise Control using Collective Initial Excitation based Distributed Parameter Estimator

Parameter convergence is desirable in adaptive control as it brings several attractive features, including accurate online modelling, exponential tracking, and robust adaptation without parameter drift. However, a strong persistent‐excitation (PE) condition must be satisfied to guarantee parameter convergence in the conventional adaptive control. This study proposes a model reference composite learning control strategy to guarantee parameter convergence without the PE condition. In the composite learning, an integral at a moving‐time window is applied to construct a prediction error, an integral transformation is derived for avoiding the time derivation of plant states in the calculation of the prediction error, and both the tracking error and the prediction error are applied to update parametric estimates. Global exponential stability of the closed‐loop system is established under an interval‐excitation condition which is much weaker than the PE condition. Compared with a concurrent learning technique that has the same aim as this study, the proposed composite learning technique avoids the usage of singular value maximisation and fixed‐point smoothing resulting in a considerable reduction of computational cost. Numerical results have verified effectiveness and superiority of the proposed control strategy.

In this paper, a novel synchronous Q-learning method is proposed for solving discrete-time linear quadratic regulator (LQR) problems. To begin with, the Bellman equation corresponding to the optimal Q-function is reformulated into a consistency equation on the parameters of the optimal Q-function and the optimal controller. Then an actor-critic structure is introduced to learn the optimal Q-function and the optimal controller online in real time by using the state samples generated by the behavior policy. Particularly, the proposed synchronous Q-learning scheme simultaneously updates the Q-function approximation and the optimal controller approximation, rather than iterating between policy evaluation and policy improvement. The proposed control scheme is proved to be uniformly ultimately bounded (UUB) under appropriate learning rates, provided that certain persistence of excitation (PE) conditions are satisfied. Besides, the PE conditions can be easily met by injecting appropriate exploration noise into the behavior policy without causing any excitation noise bias. Finally, one simulation example is provided to verify the effectiveness of the proposed synchronous Q-learning method.

This work generalizes the recently developed initial excitation (IE) based adaptive control by introducing the notion of semi-initial excitation (semi-IE), a still relaxed version of IE. Typically, classical adaptive controllers guarantee Lyapunov stability of the overall error dynamics (tracking error + parameter estimation error) and asymptotic convergence of tracking error to zero, while requiring a restrictive condition of persistence of excitation (PE) for parameter convergence. The authors' recent work on a new adaptive control architecture based on the milder IE condition guarantees parameter convergence while ensuring exponential stability of the overall error dynamics once the online verifiable IE condition is satisfied. The current work further relaxes the excitation condition by proposing the concept of semi-IE. The proposed adaptive controller is proved to guarantee convergence of the parameter estimation error to a lower dimensional manifold under the weaker semi-IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed adaptive algorithm has been shown to significantly improve the transient response of tracking error as compared to the conventional approaches.

In this paper, model reference adaptive control problem is considered with reference input dependent upon the unknown parameters of the system. Due to the uncertainty in the reference input, conventional linear-in-parameters adaptive controller cannot achieve the control objective without enforcing persistent excitation (PE). A new technique is presented for introducing an excitation signal and regulating its magnitude, dependent upon the convergence of the output tracking and parameter errors. Intelligent excitation ensures parameter convergence similar to conventional PE, but initiates only when necessary. As a result, the regulated output tracks the unknown reference input. Simulations illustrate the theoretical findings

Conditions are investigated for exponential convergence of the tracking error in feedforward adaptive systems having insufficient excitation. Particular attention is paid to the adaptive gradient algorithm with periodic excitation in the overparameterized case. A main result is that for a bounded periodic regressor, the tracking error converges exponentially without regard to parameter convergence or to the degree of overparameterization. These results weaken the persistent excitation (PE) conditions and parameter convergence conditions generally considered necessary to ensure exponential tracking convergence in this class of systems.

Designing the optimal control for the practical systems is challenging due to the unknown system dynamics and unavoidable external disturbances. In this article, the $H_{\infty } $ optimal control problem is investigated for continuous-time linear systems with unknown dynamics. The existing reinforcement learning-based $H_{\infty } $ optimal control methods require persistence of excitation (PE) condition or data storage mechanism to guarantee the convergence of the algorithms. However, PE condition is hard to be monitored online and data storage mechanism requires to store huge amounts of past system data. In order to solve these problems, the initial excitation-based reinforcement learning algorithms are presented to learn the optimal control policy under an online-verifiable initial excitation condition. The properties of the initial excitation-based reinforcement learning algorithms are analyzed, which show that the presented algorithms converge to the optimum under the initial excitation condition. Numerical analysis is provided which demonstrates the correctness of the presented algorithms.

This paper studies neural learning control with predefined tracking error bound for a marine surface vessel whose accurate dynamics could not be obtained a priori . With the introduction of an error transformation function, the constrained tracking control of the original vessel is transformed into the stabilization of an unconstrained system. A filtered tracking error is introduced based on the error transformation, and radial basis function (RBF) neural networks (NNs) are employed to approximate unknown vessel dynamics. Subsequently, stable adaptive NN control is proposed to ensure ultimate boundedness of all the signals in the closed-loop system and to guarantee prescribed tracking performances. Under persistent excitation (PE) condition, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the vessel dynamics and of storing the learned knowledge in memory. The stored knowledge is reused to develop neural learning control such that the improved control performance with faster tracking convergence rate and less computational burden could be achieved, while prescribed transient and steady-state tracking control performances are guaranteed. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

This paper presents an adaptive observer design for nonlinear systems that have parametric uncertainties in the unmeasured state dynamics. Without persistency of excitation (PE) the convergence of the state estimation error to zero is proved. Under PE conditions, uniform global asymptotic stability of the origin of the state and parameter error is shown. Furthermore, if the regressor is sufficiently smooth, uniform local asymptotic stability of the origin is proved. Two simulation examples are shown to illustrate the results.

An adaptive finite-time (FT) neural control scheme is proposed for robotic manipulators, which could guarantee transient tracking performances in the presence of model uncertainties. With the introduction of an error transformation mechanism, the original constrained manipulator system can be transformed into an unrestricted system. Moreover, the FT neural learning algorithm motivated by the estimated weights error, under persistent excitation (PE) condition, can guarantee the estimated neural weights converge to a small neighborhoods around the optimal values in finite time. Subsequently, the adaptive FT neural controller could ensure uniformly ultimate boundedness of all the signals in the closed-loop system and guarantee prescribed tracking and neural learning performances. The simulation results are given to illustrate the feasibility of the algorithm and correctness of theoretical analysis.

This paper presents a novel, safe tracking control design method that learns the parameters of an uncertain Euler-Lagrange (EL) system online using adaptive learning laws. A barrier function (BF) is first used to transform the full-state constrained EL-dynamics into an equivalent unconstrained dynamics. An adaptive tracking controller is then developed along with the parameter update law in the transformed state space such that the states remain bounded for all time within a prescribed bound. A stability analysis is developed that considers the EL-dynamics' uncertainty, yielding a semi-globally uniformly ultimately bounded (SGUUB) tracking error and the parameter estimation error. The controller design is validated in simulations using a two-link planar manipulator. The results show the proposed method's ability to track the reference trajectory while remaining inside each of the predefined state bounds.

It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this article, without the need for PE condition, we address the problem of global exponential stabilization of strict-feedback systems with mismatched uncertainties and unknown yet time-varying control gains. The resultant control, embedded with time-varying feedback gains, is capable of ensuring global exponential stability of parametric-strict-feedback systems in the absence of persistence of excitation. By using the enhanced Nussbaum function, the previous results are extended to more general nonlinear systems where the sign and magnitude of the time-varying control gain are unknown. In particular, the argument of the Nussbaum function is guaranteed to be always positive with the aid of nonlinear damping design, which is critical to perform a straightforward technical analysis of the boundedness of the Nussbaum function. Finally, the global exponential stability of parameter-varying strict-feedback systems, the boundedness of the control input and the update rate, and the asymptotic constancy of the parameter estimate are established. Numerical simulations are carried out to verify the effectiveness and benefits of the proposed methods.

Due to the complex entanglement between distributed control and distributed estimation, adaptive multiagent dynamics over leaderless directed graphs are yet not completely understood. This happens even when the adaptive dynamics are based on established tools like model reference adaptive control (MRAC). This work starts from the observation that existing MRAC-based leaderless designs stop at asymptotic consensus, lacking of any guarantee for exponential consensus or parameter identification. The main contribution of this work is to show a new design departing from the existing ones in terms of exploiting persistence of excitation (PE): the proposed design is the first one attaining exponential consensus with exponential parameter identification over leaderless directed graphs. In the special case that the unknown parameters are homogeneous, PE can be relaxed to a weaker cooperative PE (C-PE) condition. The design is illustrated and verified alongside the state-of-the-art.

The problem of parameter estimation for salient permanent magnet synchronous motors (PMSMs) is considered in this paper. It is assumed that stator currents and voltages and rotor position are measurable signals and the only known motor parameter is the number of pole pairs. The proposed estimation algorithm uses dynamic operators applied to the measurable signals to get a linear regression model with unknown motor parameters. As proven, scalar estimators that are designed for each unknown motor parameter ensure finite time convergence of estimation errors to zero. The main benefit of the proposed approach is to relax the stringent assumptions imposed on regression functions such as condition of persistent excitation (PE) and non-square integrability that are often difficult to verify in practice.

Adaptive Tracking Control of Rigid Robot Manipulators by Using Only Joint Position Measurements