具有仿射等式参数约束的自适应控制参数更新律
Parameter Update Laws for Adaptive Control with Affine Equality Parameter Constraints
AI总结：
本文提出了一种具有仿射等式约束的自适应控制参数更新律，通过约束优化问题推导出两种更新方法，并通过仿真验证了其在参数收敛和轨迹跟踪方面的有效性。
摘要：
本文开发了具有凸等式约束的自适应控制参数更新律，其中一种基于仅梯度更新，另一种则结合了同时学习（CL）更新。这些更新律通过求解具有仿射等式约束的约束优化问题而推导出来。该约束问题被重新表述为一个新的变量中的等价无约束问题，从而消除了等式约束。所得到的更新律与自适应轨迹跟踪控制器集成，实现了对未知系统参数的在线学习。建立了具有等式约束参数更新律的闭环系统的Lyapunov稳定性。通过仿真实验验证了所提出的等式约束自适应控制律的有效性，证明了其在保持参数估计约束方面的能力，实现了CL基于更新律的参数收敛到真实参数，以及在约束梯度和约束CL基于更新律中分别实现了渐近和指数跟踪性能。
英文摘要：
In this paper, constrained parameter update laws for adaptive control with convex equality constraint on the parameters are developed, one based on a gradient only update and the other incorporating concurrent learning (CL) update. The update laws are derived by solving a constrained optimization problem with affine equality constraints. This constrained problem is reformulated as an equivalent unconstrained problem in a new variable, thereby eliminating the equality constraints. The resulting update law is integrated with an adaptive trajectory tracking controller, enabling online learning of the unknown system parameters. Lyapunov stability of the closed-loop system with the equality-constrained parameter update law is established. The effectiveness of the proposed equality-constrained adaptive control law is demonstrated through simulations, validating its ability to maintain constraints on the parameter estimates, achieving convergence to the true parameters for CL-based update law, and achieving asymptotic and exponential tracking performance for constrained gradient and constrained CL-based update laws, respectively.
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