Apply classical control theory, closed-loop cybernetic feedback, decentralized Model Predictive Control (MPC), and Bellman dynamic programming to govern autonomous AI agent swarms, prevent cascading reasoning divergence, and enforce formal consensus.
Formulate and solve continuous-time and discrete-time optimal control problems for high-DoF robotic manipulators, bipedal/humanoid locomotion, and autonomous guidance systems.
Synthesize formal stability and safety certificates using Control Lyapunov Functions (CLF), Control Barrier Functions (CBF), and Robust H∞ / μ-synthesis for safety-critical dynamical and multi-agent systems under bounded disturbances.
Design multi-step Bellman backup verifiers, formal process reward models (PRM), and contraction-mapping policy gradient pipelines for frontier reasoning models and sequential decision agents.
Build massively parallel differentiable rigid-body and contact-rich simulation kernels enabling 100,000+ simultaneous closed-loop control rollouts per second on GPU clusters.
Dedicated remote part-time track for MSc/PhD candidates, recent graduates, and postdoctoral researchers from 139 indexed universities worldwide to apply their exact control theory and cybernetics specialization to frontier AI agent swarms and autonomous systems.
Exact and approximate dynamic programming, value/policy iteration, contraction mappings in Banach spaces, neuro-dynamic programming, and multi-horizon sequential decision processes.
Viscosity solutions to nonlinear first- and second-order HJB PDEs, covector adjoint equations, minimum-time/minimum-fuel optimal control, and symplectic boundary-value solvers.
Real-time receding-horizon nonlinear MPC, Differential Dynamic Programming (DDP), iterative LQR (iLQR), sequential quadratic programming (SQP), and contact-implicit trajectory optimization.
Closed-loop feedback regulation, Wiener-Bellman cybernetic feedback architectures, Control Lyapunov Functions (CLF), Control Barrier Functions (CBF-QP), and robust H∞ disturbance rejection.
Bridging classical control theory with modern foundation model post-training: verifiable multi-step reasoning rewards, differentiable physics engines (CUDA/Triton/MJX), and sim-to-real policy distillation.
| Formulation | Canonical Equation / Operator | Physical & Algorithmic Domain |
|---|---|---|
| Discrete Bellman Optimality Bellman (1957) |
V*(s) = max_{a ∈ A(s)} [ R(s,a) + γ ∑_{s′} P(s′|s,a) V*(s′) ] | Markov Decision Processes (MDPs), exact dynamic programming, contraction mapping fixed-point iteration. |
| Hamilton-Jacobi-Bellman PDE Continuous-Time Optimal Control |
∂V(x,t)/∂t + min_{u ∈ U} { ⟨∇_x V(x,t), f(x,u,t)⟩ + L(x,u,t) } = 0 | Continuous-time nonlinear trajectory optimization, aerospace guidance, viscosity solutions on manifolds. |
| Pontryagin Maximum Principle Adjoint Covector Dynamics |
ẋ = ∇_p H(x,p,u*), ṗ = −∇_x H(x,p,u*), u* = argmin_u H | Two-point boundary value problems (TPBVP), indirect trajectory optimization, minimum-time/fuel control. |
| Algebraic Riccati Equation (CARE) Kalman-Bellman LQR Dual |
A^⊤ P + P A − P B R^{-1} B^⊤ P + Q = 0, K = R^{-1} B^⊤ P | Infinite-horizon Linear Quadratic Regulation (LQR), iLQR backward Riccati recursion, Kalman filtering dual. |
| CLF-CBF Safety-Critical QP Nonlinear Cybernetic Invariance |
L_f V(x) + L_g V(x)u ≤ −c V(x), L_f h(x) + L_g h(x)u + α(h(x)) ≥ 0 | Real-time quadratic programming (QP) safety filters for bipedal humanoids, surgical robotics, and autonomous vehicles. |