Nonlinear and Adaptive Control with Applications

Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems

“…21 This approach, different from the classical adaptive method, is essentially a non-CE-based adaptive control technique that overcomes the performance limitations arising from CE-based designs. It allows for prescribed uniformly stable dynamics to be assigned to the parameter estimation error, thus leading to a modular control scheme that is much easier to tune than the one obtained from the classical adaptive approach.…”

“…That is why this approach is favored by many researchers and numerous research results are emerging in recent years. Based on Astolfi and Ortega 20 and Astolfi et al, 21 and by construction of a monotone function, a new framework to design I&I adaptive controllers for nonlinearly parameterized systems was proposed in Liu et al 22 and Wang et al 23 The I&I adaptive control method was extended to the nonlinear discrete systems case in Yalçın 24 and Yalçın and Astolfi. 25 In addition to being continuously improved in theory, this adaptive method has also be successfully applied in practice, such as single-machine infinite-bus power system with a static var compensator, 26 the underactuated quadrotor unmanned aerial vehicle, and 27 nonlinear aeroelastic system.…”

Immersion and invariance observers with time-delayed output measurements

“…In this manuscript, we study the immersion and invariance (I&I) techniques presented in [11] and [7] for designing nonlinear observers. We show how these I&I ideas may be extended when the output measurements are corrupted by constant time-delays.…”

“…We show how these I&I ideas may be extended when the output measurements are corrupted by constant time-delays. Following the design method developed in [11], we derive a general tool for constructing I&I observers in the presence of time-delays. It is important to point out that, as it is the case in the delay-free setting considered in [11], the observer design relies on the existence of two mappings, β(·) and φ(·), which must be selected to render the zero solution of the estimation error dynamics asymptotically stable.…”

Intelligent neural network design for nonlinear control using simultaneous perturbation stochastic approximation (SPSA) optimization

“…It has been also shown that neural networks trained by the simultaneous perturbation stochastic approximation (SPSA) method guarantee closed-loop stability of the estimation in the control problem considered in [6]. This paper addresses the performance analysis of the SPSA-based neural networks in the adaptive control of the TORA (Translational Oscillator with a Rotational Proof Mass Actuator) system [7] [8]. Simulation results demonstrate the potential of the proposed method.…”