Minimax control of linear systems with amplitude bounded disturbances.
Optimal control problem formulated for linear constant-coefficient system subjected to class of amplitude bounded load disturbances
TIME OPTIMAL CONTROL↗
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Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $\mathcal{\tilde{O}}$(dκlog(1/ϵ)) query complexity for a d -sparse matrix, where κ is the condition number, and ϵ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Adaptive Control for Load-Following of Boiling Water Reactors Part I: Linear Systems and Fully-Observable Dynamics
Automation control is a key strategy to improve the economic competitiveness of nuclear power plants. Not only does it help reduce operational costs, but it also extends the value proposition of these plants to nontraditional markets, including unattended operations in remote villages and space. However, the dynamics of the operating environments of nuclear reactors are subject to changes over time, and there are no widely adopted methods to ensure that the automation strategy will remain effective over the extended durations required for these applications. Adaptive control is a discipline that offers the possibility to accommodate such changes online. However, it relies on mathematical assumptions that must be respected to ensure robustness and reliability. In this work, we derive an adaptive control formulation for linear systems in which all states are observable and apply it to an instance of load-follow operation for Boiling Water Reactors. We assumed uncertainty in two factors: the temperature coefficient and the control rod worth, both of which are affected over time by the evolution of the nuclear reactor core environment. With an arbitrary penalty factor of 5, we found that the mean absolute and integral time absolute errors can be reduced by more than 90%, underscoring the strength of adaptive control. To extend the application to more challenges, different uncertainties and load-follow trajectories, as well as new formulations that include non-linearity and partial observability, are currently being developed.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems
Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine learning has motivated hardware support for half-precision floating-point arithmetic. A primary challenge in high-performance computing is to leverage reduced-precision and mixed-precision hardware. We show how the FP16/FP32 Tensor Cores on NVIDIA GPUs can be exploited to accelerate the solution of linear systems of equations Ax = b without sacrificing numerical stability. The techniques we employ include multiprecision LU factorization, the preconditioned generalized minimal residual algorithm (GMRES), and scaling and auto-adaptive rounding to avoid overflow. We also show how to efficiently handle systems with multiple right-hand sides. On the NVIDIA Quadro GV100 (Volta) GPU, we achieve a 4×-5× performance increase and 5× better energy efficiency versus the standard FP64 implementation while maintaining an FP64 level of numerical stability.
GMRES↗
Continuous parameter dependence in linear systems of differential equations.
General convergence theorem for linear differential equation systems solution sequence, discussing continuous parameter dependence
Opial, Z.↗
Linear system theory
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Callier, Frank M.↗
Failure accommodation in linear systems through self-reorganization
Self-reorganization methods for complex linear dynamic systems to compensate for component failures
Beard, R. V.↗
On 'Type L' multivariable linear systems.
The purpose of this paper is to summarize results for linear multivariable systems that are analogous to those single input single output systems which are 'type l', i.e., that contain l integrators. Both frequency domain and time-domain properties are given. Appropriate conditions that guarantee zero steady state error in tracking vector polynomial inputs are presented.
Sandell, N., Jr.↗
Linear systems design using state variable feedbacks
State variable feedback method for calculating linear automatic control systems
AUTOMATIC CONTROL↗
Analysis of piecewise linear systems by the method of integral equations.
Nonlinearities in piecewise linear automatic control systems, using integral equations
NONLINEAR SYSTEM↗
FORTRAN subroutines for out-of-core solutions of large complex linear systems
The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.
Yip, E. L.↗
Linear system identification via an asymptotically stable observer
This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer, and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples using simulated noise-free data are presented to illustrate the proposed method.
Phan, Minh↗
Identification of linear systems by an asymptotically stable observer
A formulation is presented for the identification of a linear multivariable system from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and extensive numerical examples using simulated noise-free data are presented to illustrate the proposed method.
Phan, Minh Q.↗
Models of failure in linear systems
The concept of reliability in systems theory is discussed. Emphasis is placed on identifying failed or degraded systems and constructing a strategy to control the system in the failed mode. Systems are assumed to be linear and transformations into the failed mode occur smoothly. The family into which a nominal system is embedded is examined along with the relations within the family. The class of systems into which a given system can be algebraically transformed is investigated.
Martin, C. F.↗
Effect of digitally computed drives on performance of continuous linear systems
The dependence of the Bode response upon digital sample rate for first and second order linear continuous systems driven by a digital computer is derived. Open loop lead compensation introduced within the digital computer in order to increase the system bandwidth is also examined in terms of derived Bode responses. This introduction of lead terms within the digital computer is shown to be effective at operating frequencies below the Nyquist frequency. In most practical applications, empirical determination of these lead coefficients appears to be a sufficient compensation method.
Parrish, R. V.↗
Response of discrete linear systems to forcing functions with inequality constraints.
An analysis is made of the maximum response of discrete, linear mechanical systems to arbitrary forcing functions which lie within specified bounds. Primary attention is focused on the complete determination of the forcing function which will engender maximum displacement to any particular mass element of a multi-degree-of-freedom system. In general, the desired forcing function is found to be a bang-bang type function, i.e., a function which switches from the maximum to the minimum bound and vice-versa at certain instants of time. Examples of two-degree-of-freedom systems, with and without damping, are presented in detail. Conclusions are drawn concerning the effect of damping on the switching times and the general procedure for finding these times is discussed.
Michalopoulos, C. D.↗
Open-loop-feedback-optimal adaptive stochastic control of linear systems
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
Ku, R.↗
An adaptive observer for single-input single-output linear systems
It is shown that the full order adaptive observer for single input, single output, observable, continuous, stable, linear differential systems in the absence of a deterministic or random disturbance vector guarantees the vanishing of observation error, regardless of the size of the constant or slowly varying parameter ignorance. The observer parameters are directly changed in a Liapunov adaptive way so as to eventually yield the unknown full order Luenberger observer. The observer poles throughout may be placed freely in the stable region and no derivatives are required in the adaptive law.
Carroll, R. L.↗