Yebin Wang

Optimal Codesign of Nonlinear Control Systems Based on a Modified Policy Iteration Method

This brief studies the optimal codesign of nonlinear control systems: simultaneous design of physical plants and related optimal control policies. Nonlinearity of the optimal codesign problem could come from either a nonquadratic cost function or the plant. After formulating the optimal codesign into a nonconvex optimization problem, an iterative scheme is proposed in this brief by adding an additional step of system-equivalence-based policy improvement to the conventional policy iteration. We have proved rigorously that the closed-loop system performance can be improved after each step of the proposed policy iteration scheme, and the convergence to a suboptimal solution is guaranteed. It is also shown that under certain conditions, this additional policy improvement step can be conducted by solving a quadratic programming problem. The linear version of the proposed methodology is addressed in the context of linear quadratic regulator. Finally, the effectiveness of the proposed methodology is illustrated through the optimal codesign of a load-positioning system.

On the optimal trajectory generation for servomotors: A Hamiltonian approach

This note considers the energy optimal trajectory generation of servo systems through open-loop optimal control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory.

An iterative approach to the optimal co-design of linear control systems

ABSTRACT This paper investigates the optimal co-design of both physical plants and control policies for a class of continuous-time linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimisation problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimisation algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.

Co-design of nonlinear control systems with bounded control inputs

This paper considers co-design of nonlinear constrained control systems: simultaneous design of the nonlinear plant and control policy where the control is bounded. Similar to prior art, the co-design is attacked as a non-convex optimization problem, which is solved by using an improved policy iteration scheme. We have proved rigorously that the system performance can be improved after each step of the proposed policy iteration scheme until convergence to a sub-optimal solution is attained. Effectiveness of the proposed methodology is illustrated through the co-design of a load-positioning system.

Speed sensorless state estimation for induction motors: A moving horizon approach

This paper investigates the speed sensorless state estimation problem for induction motors. Aiming at developing new state estimation means to improve the estimation bandwidth, this paper proposes various moving horizon estimation (MHE)-based state estimators. Applying the MHE for induction motors is not straightforward due to the fast convergence requirement, external torque disturbances, parametric model errors, etc. To improve speed estimation transient performance, we propose an MHE based on the full induction motor model and an assumed load torque dynamics. We further formulate an adaptive MHE to jointly estimate parameters and states and thus improve robustness of the MHE with respect to parametric uncertainties. A dual-stage adaptive MHE, which performs parameter and state estimation in two steps, is proposed to reduce computational complexity. Under certain circumstances, the dual-stage adaptive MHE is equivalent to the case with a recursive least square algorithm for parameter estimation and a conventional MHE for state estimation. Implementation issues and tuning of the estimators are discussed. Numerical simulations demonstrate that the proposed estimators can effectively estimate the induction motor states at a fast convergence rate, and the dual-stage adaptive MHE can provide converging state and parameter estimation despite the initial model parametric errors.

High gain observer for speed-sensorless motor drives: Algorithm and experiments

This paper considers the rotor speed and flux estimation for induction motors, which is one of the key problems in speed-sensorless motor drives. Existing approaches, e.g. adaptive, Kalman filter-based, and sliding mode observer, have limitations such as unnecessarily assuming the rotor speed as a constant parameter, failure to ensure convergence of estimation error dynamics, or conservative design. This paper proposes a non-triangular observable form-based estimation algorithm. This paper presents realizable observers to avoid transforming the induction motor model into the form. Advantages of the new estimation algorithm include guaranteed stability of estimation error dynamics, constructive observer design, ease of tuning, and improved speed estimation performance. Finally, experiments are conducted to demonstrate the effectiveness of the proposed estimation algorithm.

Leader-to-Formation Stability of Multiagent Systems: An Adaptive Optimal Control Approach

This note proposes a novel data-driven solution to the cooperative adaptive optimal control problem of leader-follower multiagent systems under switching network topology. The dynamics of all the followers are unknown, and the leader is modeled by a perturbed exosystem. Through the combination of adaptive dynamic programming and internal model principle, an approximate optimal controller is iteratively learned online using real-time input-state data. Rigorous stability analysis shows that the system in closed-loop with the developed control policy is leader-to-formation stable, with guaranteed robustness to unmeasurable leader disturbance. Numerical results illustrate the effectiveness of the proposed data-driven algorithm.

Cooperative optimal output regulation of multi-agent systems using adaptive dynamic programming

This paper proposes a novel solution to the adaptive optimal output regulation problem of continuous-time linear multi-agent systems. A key strategy is to resort to reinforcement learning and approximate/adaptive dynamic programming. A data-driven, non-model-based algorithm is given to design a distributed adaptive suboptimal output regulator in the presence of unknown system dynamics. The effectiveness of the proposed computational control algorithm is demonstrated via cooperative adaptive cruise control of connected and autonomous vehicles.

From reeds-shepp's paths to continuous curvature paths-Part I: Transition schemes & algorithms

This work considers real-time continuous curvature (CC) path planning for car-like robots. It is motivated by the fact that Reeds-Shepps (RS) based path planning remains unmatched in terms of computation efficiency and reliability when compared with various CC path planning results. Similar to [1], this paper post-processes RS paths to enforce the CC property, while ensuring CC paths contained in a neighborhood of the RS paths to maintain obstacle clearance. Targeting to alleviate concerns about reliability and computational efficiency, we exploit the geometric insights casted by μ-tangency conditions [2] to post-process RS paths. Specifically, distinctive postprocessing scheme is devised offline for each type of discontinuous curvature junctions. The proposed schemes, though suboptimal, are straightforward, and result in CC path planning with guaranteed completeness at the negligible increase of computation. Effectiveness of proposed schemes and resultant algorithms is validated by numerical simulations.

On extension of a gradient-based co-design algorithm to linear descriptor systems

As a holistic approach, optimal co-design of a control system determines both the plant and controller simultaneously to optimize certain performance metrics. Prior co-design work typically assume a control system in the classic state space form, and thus compromise the range of applicability. This paper considers co-design for control systems in the linear descriptor form, with the purpose to minimize the H2 norm of a closed-loop transfer function. We demonstrate that the gradient of the cost function with respect to plant parameters can be computed analytically, and thus extend the previous gradient-based co-design algorithm to the linear descriptor system case.