Control Of Large-scale Dynamical Systems Research Articles

Modeling and control of heterogeneous field robots under partial observation

The control of large-scale dynamic systems, such as field robots, requires a more modular and scalable approach than traditional control theory. Recently, we designed modular supervisory controllers for field robots in agricultural applications based on a hybrid system that combines continuous-time and discrete-event systems. We verified that the developed hybrid system could control field robots and observe all the events while meeting the behavioral specifications. In contrast, all possible events cannot be monitored by a supervisor in a real-field robot system because of the presence of sensors, noise, disturbances, and failure. Therefore, in this study, we expanded the modular supervisor presented in previous studies by considering partial observations. Specifically, we proposed a process for designing an appropriate modular supervisor by considering the observability. The experimental results demonstrated that only observable events could cause state changes, verified by dynamic simulations representing a natural field environment. The effects of the proposed hybrid system-based modeling and control methodology are discussed in light of our systematic results.

Study of the thermo-magneto-hydrodynamic flow of micropolar-nanofluid in square enclosure using dynamic mode decomposition and proper orthogonal decomposition

In the present contribution, we analyze the non-stationary, incompressible, laminar, natural convection flow in a rectangular enclosure filled with a micropolar-nanofluid (Al2O3/water) in the presence of a magnetic field, using Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) method. DMD method utilizes numerically or experimentally obtained data (often generated by nonlinear dynamics) to compute the eigenvalues and the eigenmodes of an approximated linear model, and the growth/decay (damp) rates, frequencies and spatial structures for each mode. POD provides the energy content measure for different modes. DMD and POD method have been applied in the study, optimization and control of large-scale dynamical systems. They can be used supplementary to each other or separately for cross comparison. We propose an efficient way to (i) snapshots sampling (ii) select the optimal number for analysis and (iii) define the grid resolution (grid density) for obtaining a grid independent solution for the DMD analysis. We numerically solve the flow equations using a meshless point collocation method (MPCM), using the Moving Least Square (MLS) method to approximate the unknown field functions and their spatial derivatives. We demonstrate stability of the system using the Ritz and dynamic spectrum along with the phase portrait of time coefficients of the most dominant DMD modes. We estimate the energy contents of the captured modes for various Hartman (Ha) and Rayleigh (Ra) numbers, nanoparticles volume fractions (φ), magnetic field (ξ) and square enclosure angles (γ). The energy content of each mode for Al2O3/water nanofluid is associated with the corresponding eigenvalue and discloses its contribution to the total energy. The results show that the above mentioned parameters significantly affect the energy contents of the captured modes.

Review of Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Review of Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

An SQP method for the optimal control of large-scale dynamical systems

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demonstrably more robust than single shooting. In the context of the SQP method, the use of modified multiple shooting involves a transformation of the constraint Jacobian. The affected rows are those associated with the continuity constraints and any path constraints applied within the shooting intervals. Path constraints enforced at the shooting points (and other constraints involving only discretized states) are not transformed. The transformation is cast almost entirely at the user level and requires minimal changes to the optimization software. We show that the modified quadratic subproblem yields a descent direction for the ℓ 1 penalty function. Numerical experiments verify the efficiency of the modified method.

Parallel asynchronous algorithms for optimal control of large-scale dynamic systems

This paper presents two parallel asynchronous algorithms for the solution of the optimal control problem of linear large-scale dynamic systems. These algorithms are based on the prediction concept. The first one adopts the interaction prediction approach and the second is based upon the costate prediction approach. The convergence behaviour of the proposed algorithms is thoroughly investigated. The new algorithms are applied on three practical systems and simulation results are presented and compared with those obtained using the well-known synchronous algorithms. It is shown that substantial savings in computation time can be achieved by employing the proposed asynchronous algorithms. © 1997 John Wiley & Sons, Ltd.

Decentralized control of large-scale dynamical systems incorporating feedforward compensators

A decentralized control design method for large-scale interconnected dynamical systems is presented in this paper. The method is based on decentralized implementation of centralized controllers. The decentralization is achieved by modelling the interactions among the subsystems comprising the global closed-loop feedback control system and replacing them with feedforward compensators.

Problems in Large-Scale Social Economic Systems

This paper attempts to show how complexity can defeat the analysis, prediction and control of large-scale dynamic systems. Some characteristics and facets of complexity are explored, and three research strategies are discussed which lead to a satisfactory treatment of complexity in dynamic systems. The research strategies relate to (i) the control-theoretic, hierarchical approach, (ii) the design-oriented, algebraic approach, (iii) models using catastrophe theory. The virtues of these approaches are compared, and some practical difficulties in dealing with complex systems are discussed.

Large-scale systems: stability, complexity, reliability

This paper establishes the connective stability concept in the framework of the comparison principle and vector Liapunov functions, as a natural setting for resolving the complexity vs reliability problem in the control of large-scale dynamic systems. The central result is the following: A stable complex system when composed as a competitive structure of the interconnected stable subsystems remains stable despite the on-off participation of the subsystems. This result is important in that it can be used efficiently to synthesize reliable complex systems by multilevel feedback control.

Control of large-scale dynamic systems by aggregation

A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by aggregating the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.