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Liapunov method synthesis of time variable nonlinear multivariable systems, deriving simplified control law for tracking of linear noninteracting model
Method and computer program for solving arbitrary simultaneous system of nonlinear algebraic and transcendental equations
Neighboring optimal feedback control of multi-input nonlinear dynamic systems
A technique for digital control of nonlinear stochastic plants is presented. The development achieves a practical digital algorithm with which the closed-loop system behaves in a classical Type I manner even with gross nonlinearities in the plant structure and low signal-to-noise power ratios. The design procedure is explained in detail and illustrated by an example whose simulated responses testify to the practicality of the approach.
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.
Almost periodic solutions of two nonlinear Volterra integral equations
A general procedure for the design of a digital controller for nonlinear stochastic systems is presented; the emphasis is on development of partitioned-adaptive control techniques which provide rapid tracking of the system state vector to follow rapid trajectory variations. Tests involving the control of a low-order nonlinear oscillator suggest that the procedure yields an effective method for achieving closed-loop performance, despite the difficulty of the control problem
The modifications to the design of a fault inferring nonlinear detection system (FINDS) algorithm to accommodate flight computer constraints and the resulting impact on the algorithm performance are summarized. An overview of the flight data-driven FINDS algorithm is presented. This is followed by a brief analysis of the effects of modifications to the algorithm on program size and execution speed. Significant improvements in estimation performance for the aircraft states and normal operating sensor biases, which have resulted from improved noise design parameters and a new steady-state wind model, are documented. The aircraft state and sensor bias estimation performances of the algorithm's extended Kalman filter are presented as a function of update frequency of the piecewise constant filter gains. The results of a new detection system strategy and failure detection performance, as a function of gain update frequency, are also presented.
The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.
The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.
Computational techniques for identifying linear and nonlinear mechanical systems subject to random excitation
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Detailed software documentation of the digital computer program FINDS (Fault Inferring Nonlinear Detection System) Version 3.0 is provided. FINDS is a highly modular and extensible computer program designed to monitor and detect sensor failures, while at the same time providing reliable state estimates. In this version of the program the FINDS methodology is used to detect, isolate, and compensate for failures in simulated avionics sensors used by the Advanced Transport Operating Systems (ATOPS) Transport System Research Vehicle (TSRV) in a Microwave Landing System (MLS) environment. It is intended that this report serve as a programmers guide to aid in the maintenance, modification, and revision of the FINDS software.
Numerical digital computer method for determining transient responses of nonlinear automatic systems based on calculation of convolution integral
An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.
Numerical solution of boundary value problem for nonlinear integro-differential equation system of hypersonic boundary layer
This paper presents the performance analysis results of a fault inferring nonlinear detection system (FINDS) using integrated avionics sensor flight data for the NASA ATOPS B-737 aircraft in a Microwave Landing System (MLS) environment. First, an overview of the FINDS algorithm structure is given. Then, aircraft state estimate time histories and statistics for the flight data sensors are discussed. This is followed by an explanation of modifications made to the detection and decision functions in FINDS to improve false alarm and failure detection performance. Next, the failure detection and false alarm performance of the FINDS algorithm are analyzed by injecting bias failures into fourteen sensor outputs over six repetitive runs of the five minutes of flight data. Results indicate that the detection speed, failure level estimation, and false alarm performance show a marked improvement over the previously reported simulation runs. In agreement with earlier results, detection speed is faster for filter measurement sensors such as MLS than for filter input sensors such as flight control accelerometers. Finally, the progress in modifications of the FINDS algorithm design to accommodate flight computer constraints is discussed.