Above are papers related to the following paper: [Paper_ID] Paper #18536. 	[Title] "UNIVERSAL" CONSTRUCTION OF ARTSTEIN'S THEOREM ON NONLINEAR STABILIZATION 1 [Abstract] Report SYCON-89-03 ABSTRACT This note presents an explicit proof of the theorem -due to Artstein- which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. More- over, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18532. 	[Title] A REMARK ON ROBUST STABILIZATION OF GENERAL ASYMPTOTICALLY CONTROLLABLE SYSTEMS [Abstract] It was shown recently by Clarke, Ledyaev, Sontag and Subbotin that any asymptotically controllable system can be stabilized by means of a certain type of discontinuous feedback. The feedback laws constructed in that work are robust with respect to actuator errors as well as to perturbations of the system dynamics. A drawback, however, is that they may be highly sensitive to errors in the measurement of the state vector. This paper addresses this shortcoming, and shows how to design a dynamic hybrid stabilizing controller which, while preserving robustness to external perturbations and actuator error, is also robust with respect to measurement error. This new design relies upon a controller which incorporates an internal model of the system driven by the previously constructed feedback. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1106854. 	[Title] GENERAL CLASSES OF CONTROL-LYAPUNOV FUNCTIONS [Abstract] The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov functions (clf's) defined by means of generalized derivatives. In this manner, one obtains a complete characterization of asymptotic controllability, applying in principle to a far wider class of systems than Artstein's Theorem (which relates closed-loop feedback stabilization to the existence of smooth clf's). The proof relies on viability theory and optimal control techniques. 1. Introduction. In this paper, we study systems of the general form Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1114184. 	[Title] CONTROL-LYAPUNOV FUNCTIONS FOR TIME-VARYING SET STABILIZATION [Abstract] This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #86923. 	[Title] Asymptotic Controllability Implies Feedback Stabilization [Abstract] | Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #48555. 	[Title] FEEDBACK STABILIZATION USING TWO-HIDDEN-LAYER NETS [Abstract] This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for certain problems two hidden layers are required, contrary to what might be in principle expected from the known approximation theorems. The differences are not based on numerical accuracy or number of units needed, nor on capabilities for feature extraction, but rather on a much more basic classification into "direct" and "inverse" problems. The former correspond to the approximation of continuous functions, while the latter are concerned with approximating one-sided inverses of continuous functions |and are often encountered in the context of inverse kinematics determination or in control questions. A general result is given showing that nonlinear control systems can be stabilized using two hidden layers, but not in general using just one. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #179702. 	[Title] FURTHER FACTS ABOUT INPUT TO STATE STABILIZATION "Further facts about input to state stabilization", IEEE [Abstract] Report SYCON-88-15 ABSTRACT Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #424540. 	[Title] FEEDBACK STABILIZATION OF NONLINEAR SYSTEMS [Abstract] This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. Please summarise all the given information.

Paper #18536 has the title `"UNIVERSAL" CONSTRUCTION OF ARTSTEIN'S THEOREM ON NONLINEAR STABILIZATION 1  
` and the abstract `Report SYCON-89-03 ABSTRACT This note presents an explicit proof of the theorem -due to Artstein- which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. More- over, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. 
`.
Question: Which category should Paper #18536 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #18536 has the title `"UNIVERSAL" CONSTRUCTION OF ARTSTEIN'S THEOREM ON NONLINEAR STABILIZATION 1  
` and the abstract `Report SYCON-89-03 ABSTRACT This note presents an explicit proof of the theorem -due to Artstein- which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. More- over, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. 
`.
Question: Which category should Paper #18536 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks