scholarly journals Automated formal synthesis of provably safe digital controllers for continuous plants

2019 ◽  
Vol 57 (1-2) ◽  
pp. 223-244 ◽  
Author(s):  
Alessandro Abate ◽  
Iury Bessa ◽  
Lucas Cordeiro ◽  
Cristina David ◽  
Pascal Kesseli ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Bounded Model Checking ◽  
Digital Controllers ◽  
Inductive Generalization ◽  
Physical Plant ◽  
Continuous State Space ◽  
Continuous State ◽  
Linear Differential ◽  
Time Invariant ◽  
Physical Plants

Abstract We present a sound and automated approach to synthesizing safe, digital controllers for physical plants represented as time-invariant models. Models are linear differential equations with inputs, evolving over a continuous state space. The synthesis precisely accounts for the effects of finite-precision arithmetic introduced by the controller. The approach uses counterexample-guided inductive synthesis: an inductive generalization phase produces a controller that is known to stabilize the model but that may not be safe for all initial conditions of the model. Safety is then verified via bounded model checking: if the verification step fails, a counterexample is provided to the inductive generalization, and the process further iterates until a safe controller is obtained. We demonstrate the practical value of this approach by automatically synthesizing safe controllers for physical plant models from the digital control literature.

scholarly journals Reinforcement learning versus swarm intelligence for autonomous multi-HAPS coordination

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Ogbonnaya Anicho ◽  
Philip B. Charlesworth ◽  
Gurvinder S. Baicher ◽  
Atulya K. Nagar
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Swarm Intelligence ◽  
Performance Indicators ◽  
Convergence Rates ◽  
Tuning Parameters ◽  
Continuous State Space ◽  
Continuous State ◽  
User Coverage ◽  
Better Than

AbstractThis work analyses the performance of Reinforcement Learning (RL) versus Swarm Intelligence (SI) for coordinating multiple unmanned High Altitude Platform Stations (HAPS) for communications area coverage. It builds upon previous work which looked at various elements of both algorithms. The main aim of this paper is to address the continuous state-space challenge within this work by using partitioning to manage the high dimensionality problem. This enabled comparing the performance of the classical cases of both RL and SI establishing a baseline for future comparisons of improved versions. From previous work, SI was observed to perform better across various key performance indicators. However, after tuning parameters and empirically choosing suitable partitioning ratio for the RL state space, it was observed that the SI algorithm still maintained superior coordination capability by achieving higher mean overall user coverage (about 20% better than the RL algorithm), in addition to faster convergence rates. Though the RL technique showed better average peak user coverage, the unpredictable coverage dip was a key weakness, making SI a more suitable algorithm within the context of this work.

On coupling of random walks and renewal processes

1996 ◽  
Vol 33 (1) ◽  
pp. 122-126
Author(s):  
Torgny Lindvall ◽  
L. C. G. Rogers
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Random Walk ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
One Dimensional ◽  
Continuous State Space ◽  
Continuous State ◽  
Efficient Coupling ◽  
Blackwell's Renewal Theorem

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

scholarly journals Instantaneous brain dynamics mapped to a continuous state space

NeuroImage ◽  
2017 ◽  
Vol 162 ◽  
pp. 344-352 ◽  
Author(s):  
Jacob C.W. Billings ◽  
Alessio Medda ◽  
Sadia Shakil ◽  
Xiaohong Shen ◽  
Amrit Kashyap ◽  
...  
Keyword(s):  
State Space ◽  
Brain Dynamics ◽  
Continuous State Space ◽  
Continuous State

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

scholarly journals A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems

2021 ◽  
Vol 8 (1) ◽  
pp. 1-11
Author(s):  
Abdul Abner Lugo Jiménez ◽  
Guelvis Enrique Mata Díaz ◽  
Bladismir Ruiz
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Initial Conditions ◽  
Stationary Regime ◽  
Heat Transfer Fluid ◽  
Mimetic Finite Difference Method ◽  
Linear Differential

Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

scholarly journals Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 230
Author(s):  
Juan-Carlos Cortés ◽  
Ana Navarro-Quiles ◽  
José-Vicente Romero ◽  
María-Dolores Roselló
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Random Variable ◽  
Second Order ◽  
Singular Points ◽  
Linear Differential Equations ◽  
Transformation Technique ◽  
Order Linear ◽  
Bessel Differential Equation ◽  
Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

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