Optimal Tracking Design for Sampled-Data Systems with Input Time Delay under State and Control Constraints.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H2 sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H2 sampled-data controller for the sampled-data systems with the various input time delays.

The cooperative tracking control problem for the multiagent systems with unknown dynamic models, state constraints, control input constraints, optimal performance index, and convergence rate constraints is investigated in this article. A novel design framework is proposed to cope with these constraints and requirements. More specifically, the mean value theorem is utilized to transform the control input constraint to the unconstrained form. The performance function combined with a barrier Lyapunov function is leveraged to achieve the guaranteed transient tracking performance, finite-time convergence, and state constraints. To satisfy the optimal performance index, while considering the unknown dynamics of agents, we employ the actor-critic neural network architecture to get the near-optimal solution. Our control scheme is completely model-free. The rigorous Lyapunov stability analyses show that the full-state constraints and control input constraints are always satisfied, and the cooperative tracking errors can be made as small as possible in a finite time at a desired decay rate by appropriately setting the parameters in the performance function and barrier Lyapunov function. Finally, the simulation and hardware tests are conducted to clarify the effectiveness of the proposed control strategy.

In this paper, an optimal regulator design for fractional order linear systems with input time-delay is developed.Fractional systems are very sensitive to delay so delay is a critical factor.Here the input time-delay in linear fractional-order system is applied and the response shows an improvement of less than 0.001 ms.The input time-delay is considered at the beginning of the control design and no approximation and estimation are used in the control system Thus the system performance and stability can be guaranteed.Instability in responses might occur if a system with input time-delay is controlled by an optimal regulator design for fractional linear system that was designed with no consideration of input time-delay.The transformation model which is first presented, change the optimal regulator design for fractional order linear systems with input time-delay into a system without delay formally.Simulation graphs demonstrate better performance of the proposed optimal regulator design by fractional order with consideration of the value criterion.

Optimizing multiple objectives is a common challenge in complex decision-making scenarios, where improving one objective often comes at the expense of another. In power system generation, two critical objectives must be simultaneously minimized: the total generation cost and the total emissions released. This study introduces a multi-objective optimization method developed to address these dual objectives. The proposed approach aims to identify the optimal solution to the economic dispatch problem, balancing the trade-off between minimizing generation costs and reducing environmental impact by lowering total emissions. Heuristic optimization is used to solve this multi-objective combined economic and emission dispatch (MOCEED) problems through the implementation of Multi-Objective Evolutionary Programming (MOEP). In this study, the Weighted Sum Method (WSM) is combined with the Evolutionary Programming (EP) technique to minimize both objectives. The developed approach is validated on the IEEE 30-Bus RTS, which consists of six generators. The effectiveness of the developed technique is evaluated and compared the results against scenarios without optimization. Simulations are performed using MATLAB software, and the results demonstrate that the proposed Multi-Objective Evolutionary Programming (MOEP) successfully identifies the optimal generator outputs, achieving significant reductions in both total generation cost and emissions. These results highlight the method's capability to provide superior solutions for multi-objective economic dispatch problems.

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control. The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods. Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.

Maneuver design is a vital prerequisite for autonomy in aerospace guidance and control. It ensures system safety by analyzing the feasibility of the proposed maneuvers. This paper demonstrates a holistic approach to maneuver design by emphasizing its feasibility with consideration on the complete dynamics of the system and its constraints. Computational bifurcation analysis is employed to generate a sequence of trim solutions based on specified state and control constraints that define a stipulated maneuver. Implementing this approach on a stratospheric airship model helps attempt a few of its challenging and interesting facets like autonomous hovering, ascending, and descending by gauging its performance and formulating realistic maneuvers pertaining to the imposed limitations on the lateral excursion, control, and state constraints. The effectiveness of the proposed maneuvers is then evaluated using numerical simulations with computed control schedules in an open-loop.KeywordsStratospheric airshipManeuver designAutonomy

The problem of explicitly determining the worst persistent input disturbance that a closed loop system can tolerate under prespecified state and control constraints is studied. Verification of designs specifically aimed at maximizing the size of persistent bounded disturbances while satisfying system constraints, typically requires extensive simulations because the exact nature of the worst input is not known. In this paper the exact nature of the worst input is completely characterized for both SISO and MIMO cases. A finite number of specific impulse responses of the closed loop system determines the worst persistent input disturbance. In the case of a SISO system with n state constraints (|x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> | ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ), a, control constraint (|u| ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ) and an output constraint (|y| ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ), n + 2 impulse responses are generaly needed. With this new result the large number of simulations that is typically needed for design verification can be significantly reduced. Three examples illustrate how the new characterization can be utilized.

Feedback Control of Discrete Linear Switching Systems with Bounded State and Control Input in the Presence of Disturbances

Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection

A new evolutionary programming algorithm for multi-objective optimization is proposed. It employs two elitism mechanisms and does not include fitness assignment. The proposed algorithm was applied to the mobile robot path planning with three objectives. The random approach combined with a heuristic method based on domain knowledge were used in the initialization process to motivate convergence, and three evolutionary operators named deletion, repair and smooth were designed to improve the searching efficiency of the algorithm. Simulation results indicate that the proposed algorithm can find a set of Pareto optimal solutions efficiently in a single run, from which the decision maker can make a choice.

A novel technique is proposed for output feedback control of constrained linear discrete-time causal descriptor systems. In particular, it is shown how linear state and control constraints can be satisfied by using only output measurements corrupted by unknown but bounded noise. To this end, conditions are established under which a polyhedron contained in the set defined by the state constraints can be made invariant through output feedback. The control input which enforces the constraints can be computed online through the solution of linear programming problems. The proposed technique is then applied to the control of a hydraulic three-tank system. Simulated as well as experimental results illustrate the proposed technique and indicate that it can be potentially used in practical situations.

A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The optimal control problem is transcribed into nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

Considers measurement feedback switching control of systems with state and control constraints. Prior works have proved that switching control strategies have ability to resolve a common conflict in the design of state regulators such that meeting performance objectives while simultaneously avoiding violation of constraints. However, all of such switching control strategies are derived under consideration of full state feedback. In this paper, a measurement feedback switching control law is proposed. The main idea is to utilize a set-valued estimation technique which produces a set of possible state vectors consistent with measured output data. The resulting overall controller assures that state and control constraints are satisfied using only measurement feedback.

A control scheme for electrostatically shaping a membrane is developed. The scheme achieves stabilization of the first mode of the membrane at a desired equilibrium, that may be open loop unstable, without violating specified state and control constraints. The ideas on the use of an "equilibrium-parametrized" family of Lyapunov functions to enforce state and control constraints in nonlinear systems go significantly beyond the specific example treated here. They can be widely applied in the context of Lyapunov-based designs, including nonlinear systems with disturbance inputs and uncertainties.