Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

Some new concepts in nonlinear systems

Some new concepts characterizing the response of nonlinear systems are developed. These new concepts are denoted by the terms, the transient system equivalent, the response vector, and the space-phase components. This third concept is analyzed in comparison with the well-known technique of symmetrical components. The performance of a multiplicative feedback control system is represented by a nonlinear integro-differential equation; its solution is obtained by the principle of variation of parameters. The system response is treated as a vector and is resolved into its space-phase components. The individual effects of these components on the performance of the system are discussed. The suitability of the technique for the transient analysis of higher order nonlinear control systems is discussed.

Compensator for constant relative stability in process control systems

Process control systems are designed for a closed-loop peak magnitude of 2dB, which corresponds to a damping coefficient () of 0.5 approximately. With this specified constraint, the designer should choose and/or design the loop components to maintain a constant relative stability. However, the manipulative variable in almost all chemical processes will be the flow rate of a process stream. Since the gains and the time constants of the process will be functions of the manipulative variable, a constant relative stability cannot be maintained. Up to now, this problem has been overcome either by selecting proper control valve flow characteristics or by gain scheduling of controller parameters. Nevertheless, if a wrong control valve selection is made then one has to account for huge loss in controllability or eventually it may lead to an unstable control system. To overcome these problems, a compensator device that can bring back the relative stability of the control system was proposed. This compensator is similar to a dynamic nonlinear controller that has both online and offline information on several factors related to the control system. The design and analysis of the proposed compensator is discussed in this article. Finally, the performance of the compensator is validated by applying it to a two-tank blending process. It has been observed that by using a compensator in the process control system, the relative stability could be brought back to a great extent despite the effects of changes in manipulative flow rate.

An Ensemble Kushner-Stratonovich-Poisson Filter for Recursive Estimation in Nonlinear Dynamical Systems

We propose a Monte Carlo filter for recursive estimation of diffusive processes that modulate the instantaneous rates of Poisson measurements. A key aspect is the additive update, through a gain-like correction term, empirically approximated from the innovation integral in the time-discretized Kushner-Stratonovich equation. The additive filter-update scheme eliminates the problem of particle collapse encountered in many conventional particle filters. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth.

Nonlinear Control Design for an Air-breathing Engine with State Estimation

A nonlinear control design approach is presented in this paper for a challenging application problem of ensuring robust performance of an air-breathing engine operating at supersonic speed. The primary objective of control design is to ensure that the engine produces the required thrust that tracks the commanded thrust as closely as possible by appropriate regulation of the fuel flow rate. However, since the engine operates in the supersonic range, an important secondary objective is to ensure an optimal location of the shock in the intake for maximum pressure recovery with a sufficient margin. This is manipulated by varying the throat area of the nozzle. The nonlinear dynamic inversion technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs have also been carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, an extended Kalman Filter based state estimation design has been carried out both to filter out the process and sensor noises as well as to make the control design operate based on output feedback. Promising simulation results indicate that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing system.

Optimal Nonlinear Control and Estimation for a Reusable Launch Vehicle During Reentry Phase

In this paper a nonlinear optimal controller has been designed for aerodynamic control during the reentry phase of the Reusable Launch Vehicle (RLV). The controller has been designed based on a recently developed technique Optimal Dynamic Inversion (ODI). For full state feedback the controller has required full information about the system states. In this work an Extended Kalman filter (EKF) is developed to estimate the states. The vehicle (RLV) has been has been consider as a nonlinear Six-Degree-Of-Freedom (6-DOF) model. The simulation results shows that EKF gives a very good estimation of the states and it is working well with ODI. The resultant trajectories are very similar to those obtained by perfect state feedback using ODI only.

Sequential design of decentralized control systems

Our main result is a new sequential method for the design of decentralized control systems. Controller synthesis is conducted on a loop-by-loop basis, and at each step the designer obtains an explicit characterization of the class C of all compensators for the loop being closed that results in closed-loop system poles being in a specified closed region D of the s-plane, instead of merely stabilizing the closed-loop system. Since one of the primary goals of control system design is to satisfy basic performance requirements that are often directly related to closed-loop pole location (bandwidth, percentage overshoot, rise time, settling time), this approach immediately allows the designer to focus on other concerns such as robustness and sensitivity. By considering only compensators from class C and seeking the optimum member of that set with respect to sensitivity or robustness, the designer has a clearly-defined limited optimization problem to solve without concern for loss of performance. A solution to the decentralized tracking problem is also provided. This design approach has the attractive features of expandability, the use of only 'local models' for controller synthesis, and fault tolerance with respect to certain types of failure.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called 'symplectic condition' (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Stability of control systems with time delay

To find the approximate stability limit on the forward gain in control systems with small time delay, this note suggests approximating the exponential in the characteristic equation by the first few terms of its series and using the Routh–Hurwitz criterion. This approximation avoids all the time-consuming graphical work and gives a somewhat pessimistic maximum bound for the gain constant.