Peter M. Dower
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View article: Bidirectional adversarial autoencoders for high precision metasurface design
Bidirectional adversarial autoencoders for high precision metasurface design Open
Deep learning has been a critical part of designing inverse design methods that are computationally efficient and accurate. An example of this is the design of photonic metasurfaces by using their photoluminescent spectrum as the input dat…
View article: Coverage control and function approximation via semiconcave and semiconvex duality
Coverage control and function approximation via semiconcave and semiconvex duality Open
A min-of-quadratics representation for the cost function underlying a popular approach to classical coverage control is used to motivate and develop connections to function approximation via semiconcave and semiconvex duality. By consideri…
View article: Upper and Lower Bounds for a Class of Constrained Linear Time-Varying Games
Upper and Lower Bounds for a Class of Constrained Linear Time-Varying Games Open
This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the respe…
View article: Bidirectional Adversarial Autoencoders for the design of Plasmonic Metasurfaces
Bidirectional Adversarial Autoencoders for the design of Plasmonic Metasurfaces Open
Deep Learning has been a critical part of designing inverse design methods that are computationally efficient and accurate. An example of this is the design of photonic metasurfaces by using their photoluminescent spectrum as the input dat…
View article: Gradient-enhanced deep Gaussian processes for multifidelity modelling
Gradient-enhanced deep Gaussian processes for multifidelity modelling Open
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compen…
View article: A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems
A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems Open
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe regio…
View article: Gradient-Enhanced Deep Gaussian Processes for Multifidelity Modeling
Gradient-Enhanced Deep Gaussian Processes for Multifidelity Modeling Open
View article: Computational Exploitation of Low-Dimensional Nonlinearities in Hamilton-Jacobi PDEs
Computational Exploitation of Low-Dimensional Nonlinearities in Hamilton-Jacobi PDEs Open
View article: Local Upper and Lower Bounds for a Class of Constrained Optimal Control Problems
Local Upper and Lower Bounds for a Class of Constrained Optimal Control Problems Open
View article: A Game Representation for a Finite Horizon State Constrained Continuous Time Linear Regulator Problem
A Game Representation for a Finite Horizon State Constrained Continuous Time Linear Regulator Problem Open
A supremum-of-quadratics representation for a class of extended real valued barrier functions is developed and applied in the context of solving a continuous time linear regulator problem subject to a single state constraint of bounded nor…
View article: Experimental Validation of a State-Independent Input-to-Output Stable Coverage Controller
Experimental Validation of a State-Independent Input-to-Output Stable Coverage Controller Open
Distribution of a network of mobile agents over a given region, subject to various environmental factors, is desirable for a variety of applications. This problem is referred to as the coverage control problem in the motion-coordination li…
View article: Reachability of Linear Time-Invariant Systems via Ellipsoidal Approximations
Reachability of Linear Time-Invariant Systems via Ellipsoidal Approximations Open
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, exhibit exponential computational co…
View article: A Tree Structure Approach to Reachability Analysis
A Tree Structure Approach to Reachability Analysis Open
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of dimensional…
View article: A fundamental solution concept for a family of state constrained regulator problems
A fundamental solution concept for a family of state constrained regulator problems Open
A family of continuous-time regulator problems, subject to linear time-varying dynamics and convex state constraints, is parameterized with respect to a space of semiconcave terminal costs. By embedding the state constraints into an extend…
View article: Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Open
Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are respectiv…
View article: Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control Part I: Theory
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit‐time optimal control Part I: Theory Open
This work studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for solv…
View article: Verifying Fundamental Solution Groups for Lossless Wave Equations via Stationary Action and Optimal Control
Verifying Fundamental Solution Groups for Lossless Wave Equations via Stationary Action and Optimal Control Open
View article: Exploiting characteristics in stationary action problems
Exploiting characteristics in stationary action problems Open
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectories of energy conserving systems as solutions of correspondin…
View article: Conversion of Certain Stochastic Control Problems into Deterministic Control Problems
Conversion of Certain Stochastic Control Problems into Deterministic Control Problems Open
A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. A fundamental solution …
View article: Newton’s method: sufficient conditions for practical and input-to-state stability
Newton’s method: sufficient conditions for practical and input-to-state stability Open
Newton's method is a classical iterative algorithm for the numerical computation of isolated roots of algebraic equations and stationary points of functions. While its application is ubiquitous in a plethora of fields, questions concerning…
View article: Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations
Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations Open
Existence and uniqueness results for stochastic differential equations (SDEs) under exceptionally weak conditions are well known in the case where the diffusion coefficient is nondegenerate. Here, existence and uniqueness of a strong solut…
View article: A two-player game representation for a class of infinite horizon control problems under state constraints
A two-player game representation for a class of infinite horizon control problems under state constraints Open
In this paper we give feedback laws for a class of parametrized infinite horizon control problems under state constraints. We provide a two-player representation assuming time dependent dynamics and Lagrangian and the set constraints merel…
View article: Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols
Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols Open
We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in…
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stability of networked control systems implemented on WirelessHART Open
View article: Verifying fundamental solution groups for lossless wave equations via\n stationary action and optimal control
Verifying fundamental solution groups for lossless wave equations via\n stationary action and optimal control Open
A representation of a fundamental solution group for a class of wave\nequations is constructed by exploiting connections between stationary action\nand optimal control. By using a Yosida approximation of the associated\ngenerator, an appro…
View article: Synthesis of control Lyapunov functions and stabilizing feedback\n strategies using exit-time optimal control
Synthesis of control Lyapunov functions and stabilizing feedback\n strategies using exit-time optimal control Open
This paper studies the problem of constructing control Lyapunov functions\n(CLFs) and feedback stabilization strategies for deterministic nonlinear\ncontrol systems described by ordinary differential equations. Many numerical\nmethods for …
View article: Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control
Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control Open
This paper studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for sol…
View article: Game representations for state constrained continuous time linear\n regulator problems
Game representations for state constrained continuous time linear\n regulator problems Open
A supremum-of-quadratics representation for convex barrier-type constraints\nis developed and applied within the context of a class of continuous time state\nconstrained linear regulator problems. Using this representation, it is shown\nth…
View article: Game representations for state constrained continuous time linear regulator problems
Game representations for state constrained continuous time linear regulator problems Open
A supremum-of-quadratics representation for convex barrier-type constraints is developed and applied within the context of a class of continuous time state constrained linear regulator problems. Using this representation, it is shown that …
View article: Exploiting characteristics in stationary action problems
Exploiting characteristics in stationary action problems Open
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectories of energy conserving systems as solutions of correspondin…