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Found 20 papers, 5 papers with code
Inverse Optimal Cardano-Lyapunov Feedback for PDEs with Convection
In particular, we consider some classes of partial differential equations (PDEs) with quadratic convection and counter-convection, for which the L2 norm is a control Lyapunov function (CLF) whose derivative has either a depressed cubic or a quadratic dependence in the boundary control input.
Gain-Only Neural Operator Approximators of PDE Backstepping Controllers
For the recently introduced deep learning-powered approach to PDE backstepping control, we present an advancement applicable across all the results developed thus far: approximating the control gain function only (a function of one variable), rather than the entire kernel function of the backstepping transformation (a function of two variables).
From Sontag s to Cardano-Lyapunov Formula for Systems Not Affine in the Control: Convection-Enabled PDE Stabilization
We propose the first generalization of Sontag s universal controller to systems not affine in the control, particularly, to PDEs with boundary actuation.
Towards a MATLAB Toolbox to compute backstepping kernels using the power series method
Our first contribution is the development of initial steps towards a MATLAB toolbox dedicated to backstepping kernel computation.
Convection-Enabled Boundary Control of a 2D Channel Flow
Moreover, we consider no-slip boundary conditions on the tangential velocity at the top and bottom walls of the channel, and normal velocity actuation at the top and bottom walls.
Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE
This requires an adaptive approach to PDE control, i. e., an estimation of the plant coefficients conducted concurrently with control, where a separate PDE for the gain kernel must be solved at each timestep upon the update in the plant coefficient function estimate.
Moving-Horizon Estimators for Hyperbolic and Parabolic PDEs in 1-D
In the paper we provide explicit formulae for MHEs for both hyperbolic and parabolic PDEs, as well as simulation results that illustrate theoretically guaranteed convergence of the MHEs.
Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation
The recently introduced neural operators (NO) can be trained to produce the gain functions, rapidly in real time, for each state value, without requiring a PDE solution.
Newton Nonholonomic Source Seeking for Distance-Dependent Maps
The result is semiglobal and practical, for a map that is quadratic in the distance from the source.
Neural Operators for Delay-Compensating Control of Hyperbolic PIDEs
The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output or input.
Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems
The constant convergence time is achieved due to a dependence of the feedback gain of the initial state of the system.
Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs
The designs of gains for controllers and observers for PDEs, such as PDE backstepping, are mappings of system model functions into gain functions.
Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping
While, in the existing PDE backstepping, finding the gain kernel requires (one offline) solution to an integral equation, the neural operator (NO) approach we propose learns the mapping from the functional coefficients of the plant PDE to the kernel function by employing a sufficiently high number of offline numerical solutions to the kernel integral equation, for a large enough number of the PDE model's different functional coefficients.
Machine Learning Accelerated PDE Backstepping Observers
State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers.
Simultaneous Lane-Keeping and Obstacle Avoidance by Combining Model Predictive Control and Control Barrier Functions
In this work, we combine {Model Predictive Control} (MPC) and Control Barrier Function (CBF) design {methods} to create a hierarchical control law for simultaneous lane-keeping (LK) and obstacle avoidance (OA): at the low level, MPC performs LK via trajectory tracking during nominal operation; and at the high level, different CBF-based safety filters that ensure both LK and OA are designed and compared across some practical scenarios.
Practical Prescribed-Time Seeking of a Repulsive Source by Unicycle Angular Velocity Tuning
Using the recently introduced time-varying feedback tools for prescribed-time stabilization, we achieve source seeking in prescribed time, i. e., the convergence to a small but bounded neighborhood of the source, without the measurements of the position and velocity of the unicycle, in as short a time as the user desires, starting from an arbitrary distance from the source.
Finite- and Fixed-Time Nonovershooting Stabilizers and Safety Filters by Homogeneous Feedback
Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set.
Inverse Optimal Safety Filters
CBF-QP safety filters are pointwise minimizers of the control effort at a given state vector, i. e., myopically optimal at each time instant.
Delay-Compensated Distributed PDE Control of Traffic with Connected/Automated Vehicles
For the linearized system, a novel three-branch bakcstepping transformation with explicit kernel functions is introduced to compensate the input delay.
Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper bounded by a positive constant that is independent of the initial conditions of the players, and which can be prescribed a priori by the system designer.
Optimization and Control
