A Hamiltonian approach to compute an energy efficient trajectory for a servomotor system

This paper considers a nonlinear constrained optimal control problem (NCOCP) originated from energy optimal trajectory planning of servomotor systems. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. This paper proposes a method to manage the switching cost function to establish a set of necessary conditions of an NCOCP. Specifically, a concept “sub-trajectory” is introduced to match multiple Hamiltonian due to switches in the cost function. Necessary conditions on the optimal trajectory are established as a union of conditions for all sub-trajectories and Weierstrass–Erdmann corner conditions between sub-trajectories. The set of feasible structures of optimal trajectories is further identified and represented by various state transition diagrams for the servomotor application. A decomposition-based shooting method is proposed to compute an optimal trajectory by solving multi-point boundary value problems. Simulations and experiments validate the effectiveness of the methodology and the energy saving benefit.     

A model-based supervisory energy management strategy for a 12 V vehicle electrical system

This paper describes the development, implementation, and experimental verification of a supervisory energy management strategy for the vehicle electrical system of a passenger car. The control strategy commands the alternator duty cycle such that vehicle fuel economy is optimized whilst the instantaneous load current demand is met and constraints on the system voltage and battery state of charge are satisfied.The work is based on a control-oriented model of the vehicle electrical system, experimentally validated against vehicle data. Then, a constrained global optimal control problem is formulated for the energy management of the electrical system, and analytically solved using the Pontryagin׳s Minimum Principle (PMP). The optimal solution obtained is evaluated for a range of different driving cycles and electrical load current profiles, leading to the formulation of an adaptive supervisory control strategy that is implemented and tested in vehicle.     

Optimal control of large space structures governed by a coupled system of ordinary and partial differential equations

In this paper we consider the problem of optimal regulation of large space structures in the presence of flexible appendages. For simplicity of presentation, we consider a spacecraft consisting of a rigid bus and a flexible beam. The complete dynamics of the system is given by a coupled set of ordinary and partial differential equations. We show that the solution of this hybrid system is defined in a product space of appropriate finite- and infinite-dimensional spaces. We develop necessary conditions for determining the control torque and forces for optimal regulation of attitude maneuvers of the satellite along with simultaneous suppression of elastic vibrations of the flexible beam.     

Optimal input design for parameter estimation in a single and double tank system through direct control of parametric output sensitivities

In this paper the traditional and well-known problem of optimal input design for parameter estimation is considered. In particular, the focus is on input design for the estimation of the flow exponent present in Bernoulli's law. The theory will be applied to a water tank system with a controlled inflow and free outflow. The problem is formulated as follows: Given the model structure (f, g), which is assumed to be affine in the input, and the specific parameter of interest (θ), find a feedback law that maximizes the sensitivity of the model output to the parameter under different flow conditions in the water tank. The input design problem is solved analytically. The solution to this problem is used to estimate the parameter of interest with a minimal variance. Real-world experimental results are presented and compared with theoretical solutions.     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

Optimal control of a deterministic multiclass queuing system for which several queues can be served simultaneously

We consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served.We show that the optimal sequence of modes is ordered by the rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multi-parametric QP (mpQP) to a series of problems that can be solved readily.     

Path-based approach to integrated planning and control for robotic systems: A path-based approach provides an analytical integration of robot planning and control. As a result, the task level control can be achieved, and the system is capable of coping with unexpected or uncertain events

Our newly developed event-based planning and control theory is applied to robotic systems. It Introduces a suitable action or motion reference variable other than time, but directly related to the desired and measurable systems output, called event. Here the event is the length of the path tracked by a robot. It enables the construction of an integrated planning and control system where planning becomes a real-time closed-loop process. The path-based integration planning and control scheme is exemplified by a single-arm tracking problem. Time and energy optimal motion plans combined with nonlinear feedback control are derived in closed form. To the best of our knowledge, this closed-form solution was not obtained before. The equivalence of path-based and time-based representations of nonlinear feedback control is shown, and an overall system stability criterion has also been obtained. The application of event-based integrated planning and control provides the robotic systems the capability to cope with unexpected and uncertain events in real time, without the need for replanning. The theoretical results are illustrated and verified by experiments.