Fatemeh Alvankarian, Ahmad Kalhor, Mehdi Tale Masouleh
{"title":"Optimal Control Using IsoCost-Based Dynamic Programming","authors":"Fatemeh Alvankarian, Ahmad Kalhor, Mehdi Tale Masouleh","doi":"10.1049/cth2.70014","DOIUrl":"https://doi.org/10.1049/cth2.70014","url":null,"abstract":"<p>In this paper, a novel data-driven optimal control method based on reinforcement learning concepts is introduced. The proposed algorithm performs as a workaround to solving the Hamilton–Jacobi–Bellman equation. The main concept behind the proposed algorithm is the so-called IsoCost hypersurface (ICHS), which is a hypersurface in the state space of the system formed by points from which a specific amount of cost is spent by the control strategy in order to asymptotically stabilize the system. The fact that the control strategy requires to spend equal costs in order to stabilize all points on an ICHS is the reason for the naming of the IsoCost concept. Additional assumptions and definitions are mentioned before providing the theory of ICHS optimality. This theory proves, by contradiction, that the ICHS corresponding to the optimal control policy surrounds the ICHSs corresponding to other non-optimal control solutions. This paves the path to finding the optimal control solution using dynamic programming. The proposed method is implemented on the linear, fixed-base inverted pendulum, cart-pole and torsional pendulum bar system models and the results are compared with that of literature. The performance of this method in terms of cost, settling time and computation time is shown using numeric and illustrative comparisons.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143456139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adaptive Vibration Control of the Moving Cage in the 4 \u0000 \u0000 ×\u0000 $times$\u0000 4 Hyperbolic PDE-ODE Model of the Dual-Cable Mining Elevator","authors":"Elham Aarabi, Mohammadali Ghadiri-Modarres, Mohsen Mojiri","doi":"10.1049/cth2.70007","DOIUrl":"https://doi.org/10.1049/cth2.70007","url":null,"abstract":"<p>This paper proposes an adaptive output-feedback boundary control scheme to stabilize the vibrations of the moving cage in the dual-cable mining elevator system assuming the damping coefficients of the cage axial and roll motions are unknown. The mathematical formulation of the system in the Riemann coordinates is described by a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>×</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$ 4times 4$</annotation>\u0000 </semantics></math> hyperbolic partial differential equation (PDE) on a time-varying domain coupled with an ordinary differential equation (ODE) anti-collocated with the control input. At first, the nominal non-adaptive output feedback scheme is formulated by composing a state-feedback controller with the PDE state observer, utilizing the infinite-dimensional backstepping technique. Specifically, we apply two backstepping transformations to design the nominal state-feedback controller. This significantly facilitates the adaptive solutions of the backstepping kernel equations, when unknown parameters are replaced by their time-varying estimates. Then, a Lyapunov-based approach is followed to design the update laws for the unknown damping coefficients and to prove the closed-loop stability. It is shown that all states in the closed-loop system are uniformly bounded and the cage dynamics is asymptotically stable. A numerical simulation is presented to demonstrate the performance of the proposed controller.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.70007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143456137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}