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### Problem Solving

C. STOREY
1968 Nature
The first chapter introduces quasilinearization and invariant bedding and contrasts these with the classical techniques for solving bounda~y value problems.  ...  An important source of numerica l two-point boundary value problems occurs in the application of the calculus of variations and the maximum principle of Pontryagin to optimal control theory.  ...

### Robust Control for Nonlinear Discrete-Time Systems with Quantitative Input to State Stability Requirement

Shoudong Huang, Steven Weidong Su
2008 IFAC Proceedings Volumes
By introducing the concept of ISS control invariant set, a sufficient condition for the problem to be feasible is given.  ...  The objective of the control is to minimize a performance function while guaranteeing a prescribed quantitative input to state stability (ISS) property for the closed-loop systems.  ...  However, the control problems are still infinite time horizon optimal control problems which are difficult to solve.  ...

### Page 5291 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews
The set of controlled invariant flags (CIF) contains the set of CIS and inherits its most important property—the structure of an upper semilattice, which allows one to define the upper bound of a set of  ...  We study the properties of the control operator and formulate necessary and sufficient conditions for the solvability of the problem.  ...

### Page 6720 of Mathematical Reviews Vol. , Issue 87k [page]

1987 Mathematical Reviews
87k:93054 Summary: “We define the concepts of conditioned invariant and locally conditioned invariant distributions for nonlinear systems and show how they can be used to solve the problem of track- ing  ...  The concept of (A, B)-invariance has become a key tool in solving various control problems, among them ones involving disturbance decoupling.  ...

### Page 6002 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews
The authors prove that the main theorem can be extended to submodules y of R” with the property that all their invariant factors are equal.  ...  The problem of noninteraction with stability via dynamic state feedback is addresssed and solved for a class of nonlinear Hamil- tonian systems.  ...

### Controller Synthesis for Robust Invariance of Polynomial Dynamical Systems using Linear Programming [article]

Mohamed Amin Ben Sassi, Antoine Girard
2011 arXiv   pre-print
We propose a computational method to solve this problem.  ...  In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints.  ...  We propose a computational method to solve this problem. We use parameterized template expressions for the controller and the invariant.  ...

### Generalized Signal Decoupling Problem with Stability for Discrete-Time Systems

P. Barbagli, G. Marro, D. Prattichizzo
2001 Journal of Optimization Theory and Applications
Conditions for the PSDP to be solved, given in [12, 9, 1] , do not care about dimensionality of the resolving controlled invariant subspace.  ...  In [1], Estrada and Malabre proposed a synthesis procedure to solve the PSDP problem with stability using the minimum number of required differentiators for the signal to be decoupled.  ...  H V and H S are basic to synthesize the controller solving Problem 1 as discussed in Section 4.  ...

### A model reduction scheme with preserved optimal performance

Mark Mutsaers, Siep Weiland
2011 IEEE Conference on Decision and Control and European Control Conference
This paper addresses a problem in control relevant model reduction.  ...  More specifically, a model reduction scheme is proposed that preserves the disturbance decoupling property of the to-be-reduced plant.  ...  INTRODUCTION One of the most compelling applications of model reduction is to facilitate the synthesis of model based controllers for plants of high complexity.  ...

### Synthesizing Switching Logic Using Constraint Solving [chapter]

Ankur Taly, Sumit Gulwani, Ashish Tiwari
2008 Lecture Notes in Computer Science
Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem.  ...  Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property.  ...  Instead we use constraint solving to find an inductive controlled invariant set.  ...

### Synthesizing switching logic using constraint solving

Ankur Taly, Sumit Gulwani, Ashish Tiwari
2010 International Journal on Software Tools for Technology Transfer (STTT)
Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem.  ...  Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property.  ...  Instead we use constraint solving to find an inductive controlled invariant set.  ...

### Invariant-Based Safety Assessment of FPGA Projects: Conception and Technique

Vyacheslav Kharchenko, Oleg Illiashenko, Vladimir Sklyar
2021 Computers
The second type of invariants is formed based on an analysis of the specifics of a particular FPGA project and reflects the features of the tasks to be solved, the algorithms that are implemented, the  ...  Safety assessment is based on special invariants, e.g., properties which remain unchanged when a specified transformation is applied.  ...  This problem is solved with the help of the invariant calibration.  ...

### Page 3810 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews
The results are used to solve the disturbance rejection problem over PID.  ...  As the last property is important in many applications, the authors present a geometric characterization of this property.  ...

### Page 5371 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews
José Goncalves (Porto) 87i:93078 Grizzle, Jessy W. (1-IL-D) 87i:93079 Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problem. IEEE Trans.  ...  problem is solved in terms of them.  ...

### Page 697 of Automation and Remote Control Vol. 25, Issue 6 [page]

1964 Automation and Remote Control
also of their application to prac- tical problems [143-144].  ...  In recent years a new variational approach to invariance problems has been proposed [145], and the problems of “strong” and “weak” invariance have been stated and solved for a wide class of linear and  ...

### Page 4246 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews
This multichannel embedding is applicable provided a certain block shift invariance property pre- vails. Various applications are considered.  ...  Summary: “This paper is concerned with an H,, robust suboptimal control problem for linear time-invariant systems with structural uncertainties.  ...
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