Port-Hamiltonian Systems in Adaptive and Learning Control: A Survey

Abstract

Port-Hamiltonian (PH) theory is a novel, but well established modeling framework for nonlinear physical systems. Due to the emphasis on the physical structure and modular framework, PH modeling has become a prime focus in system theory. This has led to a considerable research interest in the control of PH systems, resulting in numerous nonlinear control techniques. General nonlinear control methodologies are classified in a spectrum from model-based to model-free, where adaptation and learning typically lie close to the end of the range. Various articles and monographs have provided a detailed overview of model-based control techniques on PH models, but no survey is specifically dedicated to the learning and adaptive control methods that can benefit from the PH structure. To this end, we provide a comprehensive review of the current learning and adaptive control methodologies that have been adapted specifically to PH systems.After establishing the required theoretical background, we elaborate on various general machine learning, iterative learning, and adaptive control techniques and their application to PH systems. For each method we highlight the changes from the general setting due to PH model, followed by a detailed presentation of the respective control algorithm. In general, the advantages of using PH models in learning and adaptive controllers are: i) Prior knowledge in the form of a PH model speedup the learning. ii) In some instances new stability or convergence guarantees are obtained by having a PH model. iii) The resulting control laws can be interpreted in the context of physical systems. We conclude the paper with notes on open research issues.• Learning can avoid the need for solving complex mathe-0018-9286 (c)

Efficient learning from adaptive control under sufficient excitation

“…It follows from the illustration in Figure 1 that while the excitation is weak with e ≤ , one has = 0 in (4) such that all OHD are utilized to enhance parameter convergence; while the excitation is strong with e ≥̄, the filtering of (4) works under the largest forgetting rate 0 to cope with a possibly time-varying . Therefore, under the design of in (7), OHD are collected without forgetting until the SE condition ∫ t 0 Φ ( )Φ T ( )d ≥ I in Definition 3 is satisfied. Once the SE condition is satisfied at t = T e , the excitation information will be stored in the matrix Θ of (4) as long as e ≤ ( = 0) and will be updated by (4) to cope with a possibly time-varying while e > ( > 0).…”

“…The choice of and̄in Figure 1 has been discussed in Remark 3. The choice of the other parameters in the proposed parameter learning scheme can follow the following rules: (i) The filtering constant in (3) is chosen by considering the noise strength and high-frequency unmodeled dynamics 8(section 5.7.3) ; (ii) increasing the learning rate matrix Γ in (5) speeds up parameter convergence at the cost of increasing the required sampling frequency; (iii) increasing the maximal forgetting rate 0 in (7) improves the ability to handle parameter variations but reduces the speed of parameter convergence. Remark 6.…”

“…Consider the adaptive control system constituted by (10) and (13) with the state prediction model (3), where Θ, , and are given by (4), (6), and (7), respectively. If there exist constants , T e ∈ ℝ + such that the SE condition ∫…”

“…As a major control technique of handling parametric uncertainties, adaptive control still remains among the most active research fields in the control community. [1][2][3][4][5][6][7] Usually, adaptive control only achieves asymptotic convergence of tracking errors and does not guarantee convergence of parameter estimation errors without a condition termed persistent excitation (PE). 8 Parameter convergence in adaptive control is desirable as it enhances the overall stability and robustness properties of the closed-loop system, 9 where the robustness properties result from closed-loop exponential stability, and detailed analysis can be referred to the work of Sastry and Bodson.…”

An Energy-Based Control Strategy for Battery Energy Storage Systems: A Case Study on Microgrid Applications

“…Recently the energy-based (EB) method employing the port-controlled Hamiltonian (PCH) principle has attracted more and more attention [17][18][19]. This method is a novel nonlinear robust control strategy based on passivity theory.…”