Conventional Adaptive Laws Research Articles

Output-feedback binary adaptive control of MIMO systems using monitoring function

The problem of adaptive control design for multivariable linear time-invariant plants with unknown control direction is considered. A solution is proposed based on the SDU factorization of the high frequency gain matrix (HFG) and the monitoring function approach. The adaptation scheme is the binary model reference adaptive control (BMRAC) which utilizes parameter projection and sufficiently high adaptation gains. The signs of the leading principal minors of the HFG define the control directions, and the lack of knowledge of which is a major challenge in the multivariable framework. The role of the monitoring function is to monitor the output error transient and then provide the necessary changes of the adaptation gain signs to guarantee a stable adaptive control. In addition to proving the signal boundedness of the resulting closed-loop system, the output tracking error is shown to be asymptotically as well as exponentially practically stable, i.e., exponentially stable with respect to a small residual compact set of size inversely proportional to the BMRAC adaptation gain. The latter implies good transient properties of the output tracking error in contrast to conventional adaptive laws which only guarantee asymptotic stability but can lead to extremely slow error convergence. The extension of the proposed approach to matched disturbances is also briefly discussed following the classical paradigm of disturbance estimators. Numerical results with a visual servoing application illustrate the efficiency of the proposed method.

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.

Adaptive Neural Tracking Control of Robotic Manipulators with Guaranteed NN Weight Convergence

Although adaptive control for robotic manipulators has been widely studied, most of them require the acceleration signals of the joints, which are usually difficult to measure directly. Although neural networks (NNs) have been used to approximate the unknown nonlinear dynamics in the robotic systems, the conventional adaptive laws for updating the NN weights cannot guarantee that the obtained NN weights converge to their ideal values, which could degrade the tracking control response. To address these two issues, a new adaptive algorithm with the extracted NN weights error is incorporated into adaptive control, where a novel leakage term is superimposed on the gradient method. By using the Lyapunov approach, the convergence of both the tracking error and the estimation error can be guaranteed simultaneously. In addition, two auxiliary functions are introduced to reformulate the robotic model for designing the adaptive law, and a filter operation is used to avoid measuring the acceleration signals. Comparisons to other well-recognized adaptive laws are given, and extensive simulations based on a 2-DOF SCARA robotic system are given to verify the effectiveness of the proposed control strategy.