Multi-objective control of a full-car model using linear-matrix-inequalities and fixed-order optimisation

In this paper, we develop a multi-objective model to optimally control the lead time of a manufacturing system, using goal attainment method. The manufacturing system is modelled as a new queueing system based on the failure rate of products, in which the products may have quality problems and need to be repaired in each service station. It is assumed that the product order arrives according to a Poisson process. In each service station, there is only one server (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The maintenance time of manufacturing and assembly operations is exponentially distributed. By using the total probability decomposition and Markov process method, the Queue Length Distribution, the recursion expression of the equilibrium distribution and the mean waiting time are obtained. Then, we develop a multi-objective optimal control problem, in which the average lead time, the maintenance costs and the operating costs of the system per period are minimized using goal attainment method.

In this paper, we extend the notions of $$(\Phi ,\rho )$$ ( ? , ? ) -invexity and generalized $$(\Phi ,\rho )$$ ( ? , ? ) -invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under $$(\Phi ,\rho )$$ ( ? , ? ) -invexity.

To comply with the effluent standards and growing demands for safety and reliability, the operation of wastewater treatment processes (WWTPs) has been considered as a multiobjective control problem. In this article, a data-driven multiobjective predictive control (MOPC) method is developed to deal with the conflicting control objectives to improve the operation performance of WWTPs. The main contributions of MOPC are three folds: first, a multiobjective control strategy is developed in the design of MOPC. And an adaptive fuzzy neural network identifier, using the relevant process data, is designed to catch the nonlinear behaviors of WWTPs. Second, a transfer multiobjective optimization algorithm (TMOOA) is developed to obtain the optimal solutions of the conflicting control objectives. The major advantage of TMOOA is its low computational cost, which is realized by avoiding the computation of Pareto fronts. Third, the stability of MOPC has been given in detail. Meanwhile, the benefits and feasibility of MOPC are confirmed on the benchmark simulation model no. 2. The results further demonstrate the effectiveness of the proposed control method.

This paper proposes a robust controller for semi-active suspension system with actuator dynamics using the quantitative feedback theory. It solves the vehicle vibration attenuation problem using the novel cascade approach. The proposed cascade quantitative feedback theory control approach consists of the inner and outer loop. The damping force tracking of the magneto-rheological damper is chosen as the inner loop, while the outer loop is for the vibration attenuation. The inner loop is added to the control structure to enhance damping force tracking capabilities. The damping force of the magneto-rheological damper depends on the many factors, such as the complex and nonlinear (hysteresis) dynamics and operating temperature. The actuator (magneto-rheological damper) dynamics is well approximated by a first-order model with an uncertain time constant which captures the essential dynamics. The simulation case study is conducted on a realistic quarter car suspension system to show the effectiveness of the proposed cascade control method. The proposed method is found to deliver superior performances, in terms of ride comfort and road holding, over the skyhook, [Formula: see text] control, and single-loop quantitative feedback theory control under the bump, sine, and random road disturbances.

Multi-objective H2/H∞/Impulse-to-Peak Control of a Space Launch Vehicle

Multiobjective Control Problem with Generalized Invexity

This paper is concerned with the mixed H 2 /H ∞ control problem. In general, multi-objective control problems are difficult to be solved theoretically. This is because they are not convex programming problems. In this paper, we propose an exterior-point approach for obtaining a feasible solution of the mixed H 2 /H ∞ control, which produces a controller sequence starting from an infeasible region to a feasible one. One feature of our algorithm is to be able to use any stabilizing controllers as an initial point. A numerical example is given to show the efficiency of our algorithm.

In this paper, multi-objective control of a quarter-car suspension system subjected to random road disturbances is studied. The active suspension problem is formulated as a mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synthesis problem and solved using linear matrix inequalities. It is first demonstrated that the influence of tire damping on the closed-loop performance can be significant. Then, this result is extended to suspension models with polytopic tire damping uncertainties.

Acid pre-treatment of bagasse is performed in a batch reactor, in which concentration of components evolve over time. This type of systems is usually studied using optimal control, which is concerned with dynamic systems and their optimization over time. This study applies the theory of optimal control for multi-objective optimization. The objectives include maximization of xylose and acid soluble lignin (ASL) fraction, which is obtained during acid pre-treatment. The Pontryagin's maximum principle in combination with the numerical method of steepest descent of Hamiltonian is used to solve multi-objective optimal control problem. The results showed that maximum xylose and acid soluble lignin (ASL) yield was obtained around 0.79 (g/g of xylan) and 0.3 (g/g of lignin), respectively, at final time (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> =300 min.). However, acid pre-treatment is influenced by various sources of uncertainties. Therefore, it is essential to optimize the acid pre-treatment process after considering these variabilities. In this work, variability in feedstock composition has been considered, and the stochastic maximum principle is used to perform stochastic multi-objective optimal control problem. Deterministic and stochastic control profiles were obtained for different weights. An open loop simulation of Ito model, using deterministic and stochastic control profile, was performed for 1000 samples and statistics were generated by assuming normal distribution with 95% confidence bound.

This paper proposes a multi-objective predictive control based on fuzzy satisfactory goal programming. For the different control goals, the multi-objective predictive control problem with priority is formulated. In order to acquire the preferred result, the fuzzy satisfactory goal programming for three types of fuzzy relations is presented. The released order of the satisfactory degrees is modelled to replace priority according to that the higher priority achieves the higher satisfactory degree. The balance between optimization and priority is realized by regulating the parameter. The example shows the proposed method's effectiveness.

Broadband Active Noise Control Design through Nonsmooth H∞ Synthesis

This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality reduction and extrapolation. This strategy overcomes parameter constraints by enabling adaptive dynamic adjustment of the extrapolation/proximal parameters (αk, βk, μk). Under the Kurdyka–Łojasiewicz framework for nonconvex and nonsmooth optimization, we prove the global convergence and linear convergence rate of the proposed algorithm. Additionally, through numerical experiments using synthetic and real data in matrix completion problems, we validate the superior performance of the proposed method over well-known methods.

A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H/sub 2/ tracking performance, H/sub /spl infin// tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H/sub /spl infin// PID tracking control design with regional pole constraints and mixed H/sub 2//H/sub /spl infin// PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically.

The simulation of occasional road disturbances for studying mobile vehicles dynamics