Simultaneous design and control under uncertainty: A back-off approach using power series expansions

The numerical method to solve simultaneous design and control optimization problems is considered. Firstly, the simultaneous optimization problem dealt with in this paper is defined, and this problem is transformed into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in a new formulation named Block Diagonal Hessian (BDH) method. Secondly, the BDH method is applied to the simultaneous spaceplane design and trajectory optimization problem, where the best size and its optimal trajectory are estimated to realize it. Through the several calculations, it is confirmed that the proposed BDH method is effective for simultaneous design and control optimization problems.

Integration of Design and Control Using Efficient PSE Approximations

This work presents a new methodology for the simultaneous process flowsheet and control design of dynamic systems under uncertainty using a model predictive control (MPC) strategy. Although several...

In recent years, multilayer neural networks and recurrent networks have emerged as important components for representing nonlinear transformations and have proved particularly successful in pattern recognition and optimization problems. The authors explore methods for incorporating such networks in adaptive systems for the identification and control of complex nonlinear dynamical systems. >

Dynamic Inherent Safety Analysis of a Distillation Column under Simultaneous Design and Control

In the Validation procedure proposed by the ASME V&V 20 Standard, the quantification of the modeling error of mathematical models solved by Computational Fluid Dynamics (CFD) requires the estimation of the experimental, numerical and parameter uncertainties. In its simplest form, these uncertainties are assumed independent. Parameter uncertainty is typically a consequence of lack of exact values for the boundary conditions and/or fluid properties. Its evaluation is handled by the broad field of uncertainty quantification. However, this evaluation requires simulations that are unavoidably affected by numerical errors. Therefore, it may be questionable if parameter and numerical uncertainties are really independent or, alternatively, how small must be the numerical uncertainty to estimate parameter uncertainties without its influence. In this paper we address the relation between parameter and numerical uncertainties using two test cases: the transition from laminar to turbulent flow on a flat plate at a Reynolds number of 107; the flow around the Eppler 387 airfoil at an angle of attack of 1o and Re = 3 × 105. The mathematical model for the three cases is the Reynolds-Averaged Navier-Stokes equations supplemented by the k–ω SST eddy-viscosity turbulence model and the one-equation γ transition model. Sensitivity coefficients are determined for the selected quantities of interest using the local sensitivity method and finite-differences. These estimates are performed for different levels of grid refinement to check its dependency on the estimated numerical error obtained from power series expansions. Results obtained in this study suggest that the evaluation of the parameter uncertainty only becomes independent of the numerical error when the simulation results are in the asymptotic range.

: Chemical model systems were studied to develop insights into the behavior and control of spatiotemporal dynamical systems. Noise supported wave propagation has been characterized as well as power-law relations that are characteristic of avalanche behavior. Studies were also carried out of periodically driven excitable media, spatial symmetry breaking, and the evolution of three-dimensional scroll waves. Theoretical studies were carried out on exclusive product selectivity and self-segregation in systems with competitive autocatalysis as well as coherent structure analysis of spatiotemporal chaos. Topographic organization of Hebbian neural connections, uncertain destination dynamics in coupled Lorenz systems, and normal modes for chemical reactions from time series analysis were also studied.

Dynamic systems such as robots, autonomous vehicles, and process plants require careful design and control to achieve optimal performance. This paper presents an integrated framework for the simultaneous optimization of system design parameters and control policies. The underlying mathematical formulation utilizes optimization techniques to find the best system configuration and control strategy according to specified objectives. These objectives may include metrics such as tracking error, energy consumption, safety margins, and cost. Both model-based and data-driven techniques are explored for learning the system dynamics and synthesizing optimal controllers. The optimization algorithms leveraged include gradient-based methods, evolutionary algorithms, and reinforcement learning. The benefits of the joint optimization approach are demonstrated through case studies on representative dynamic systems. Results show that the integrated design and control framework outperforms sequential optimization, leading to improved efficiency, responsiveness, and robustness. This underscores the importance of co-optimizing design and control parameters, especially for complex, uncertain systems. The proposed methods provide an effective tool for next-generation automated design of smart, adaptable systems.

Takagi-Sugeno (T-S) fuzzy model is a system described by a set of fuzzy if-then rules which give local linear representations of the underlying nonlinear system. Usually, a fuzzy control law is constructed by a set of controllers for each local linear representation to carry out the control of a T-S fuzzy system. While, simultaneous control addresses the stability and performance of multiple plants under a single feedback controller. In this paper, simultaneous linear control for nonlinear uncertain systems described by general T-S fuzzy model is considered. A procedure for simultaneous control of T-S fuzzy systems with parametric uncertainties is presented, by which robust reliability method is adopted to deal with uncertainties. Simultaneously linear controller design for an uncertain T-S fuzzy system is carried out by solving a problem of robust reliability based optimization, in which, both the robustness with respect to uncertainties and the control cost can be taken into account simultaneously. It is demonstrated by numerical simulation of the chaotic Lorenz system control that the presented method is effective and feasible.

Simultaneous design and control optimisation under uncertainty

Linear quadratic regulator (LQR) and proportional-integral-derivative (PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions. The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.

While design optimization has been employed effectively in the past few years to address the integration of design and control, the implementation of advanced model-based control techniques in such a framework has largely been ignored despite their advantages. The reason is that the advanced control schemes involve solving an optimization problem on-line, leading to a drastic increase in the complexity of the design framework. In this work a novel method is presented for integrating advanced model-based predictive controllers in a simultaneous process and control design methodology. Parametric programming is used for the controller derivation, giving rise to an explicit controller structure and removing the need for solving an optimization problem online. The resulting parametric controller is readily incorporated in the design optimization framework, bringing about significant economic and operability benefits. The key features and advantages of our approach are highlighted via binary distillation and evaporator motivating examples.

Optimal Design and Control of a Multiscale Model for a Packed Bed Chemical-Looping Combustion Reactor

This paper deals with the precision control of tumbling multibody systems with uncertainties present in the descriptions of their mathematical models. A generic tumbling multibody system consisting of a rigid body with internal degrees of freedom is used. A two-step control methodology is developed. First, a nominal system is conceived that best approximates the actual physical system. An analytical dynamics-based control methodology is used to obtain the nominal control force that ensures that this nominal system satisfies the control requirements. This is done using the control methodology proposed by Udwadia (“Optimal Tracking Control of Nonlinear Dynamical Systems,” Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 464, 2008, pp. 2341–2363). Second, an additional compensating generalized control force is designed to ensure that the actual controlled (uncertain) system tracks the trajectories of the nominal system so that the control requirements are also met by the actual system. This paper deals primarily with the second step and its combination with the first. Uncertainties in both the description of the system as well as the forces acting on it are considered. No linearizations or approximations are made in either of the steps, and the full nonlinear dynamical system is considered. The efficacy of the control methodology is demonstrated by applying it to two tumbling uncertain multibody dynamical systems.

Nonlinear Multi-Criteria Optimization for the Integrated Design and Control of Bioprocesses