Toward Adaptive Cooperation: Model-Based Shared Control Using LQ-Differential Games

The paper formulates the identification program (13) with strictly positive, homogeneous constraints ILθ(i)>0 and R(ii)>0, and then asserts uniqueness because M(i)^T M(i)>0, later noting only that M(i)^T M(i)≥0 in practice. As posed, the feasible set is an open cone, so the quadratic objective can be driven to 0 along rays without attainment; a minimizer need not exist unless a normalization or lower bounds are added. The paper does not state such a normalization, so the ‘uniqueness’ claim is unsubstantiated for (13) as written . For stability of the adaptation (15), the paper proposes checking eigenvalues at each time (a numerical test), but gives no proof. The model supplies a Lyapunov-based argument that yields a uniform exponential stability bound under explicit, reasonable hypotheses (bounded piecewise-continuous gains, existence of coupled Riccati solutions, and uniform bounds on Q(a)+Q(h) and P(a)+P(h)), filling the theoretical gap left by the paper’s qualitative discussion . The numerical example in the paper provides concrete matrices and simulations, but the model did not run them; this does not affect the theoretical reconciliation.