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State vector

About: State vector is a research topic. Over the lifetime, 5479 publications have been published within this topic receiving 103755 citations.


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Book ChapterDOI
TL;DR: The prospects for a mathematical science of computation is discussed and it is shown that from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler's laws.
Abstract: In this paper I shall discuss the prospects for a mathematical science of computation. In a mathematical science, it is possible to deduce from the basic assumptions, the important properties of the entities treated by the science. Thus, from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler’s laws.

546 citations

Journal ArticleDOI
TL;DR: It is shown that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs.
Abstract: For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.

516 citations

Journal ArticleDOI
TL;DR: An observer-based mode-dependent control scheme is developed to stabilize the resulting overall closed-loop jump system and is utilized to eliminate the effects of sensor faults and disturbances.

514 citations

Journal ArticleDOI
TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.
Abstract: 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.

505 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202348
2022127
2021196
2020291
2019317
2018292