arXiv subjects

Masoud S. Sakha

Publications and source records attributed to Masoud S. Sakha.

4 recordsLinked to original sources

arXiv2026

Switching Observers for Linear Systems: Beyond Individual Observability

This paper develops an LMI-based switching observer for linear time-invariant systems with two output channels, where only one output is available at any given time. We assume that the system is observable when both outputs are considered together, and that the time intervals between consecutive output switches are uniformly bounded. Under these assumptions, we design a set of channel-dependent Luenberger observer gains offline via linear matrix inequalities and show that the resulting switched observer drives the estimation error to zero. The main contribution is an offline gain design and convergence result for switched observers that does not require individual output channels to be detectable.

eess.SY↗

arXiv2026

Stability and Sensitivity Analysis of Relative Temporal-Difference Learning: Extended Version

Relative temporal-difference (TD) learning was introduced to mitigate the slow convergence of TD methods when the discount factor approaches one by subtracting a baseline from the temporal-difference update. While this idea has been studied in the tabular setting, stability guarantees with function approximation remain poorly understood. This paper analyzes relative TD learning with linear function approximation. We establish stability conditions for the algorithm and show that the choice of baseline distribution plays a central role. In particular, when the baseline is chosen as the empirical distribution of the state-action process, the algorithm is stable for any non-negative baseline weight and any discount factor. We also provide a sensitivity analysis of the resulting parameter estimates, characterizing both asymptotic bias and covariance. The asymptotic covariance and asymptotic bias are shown to remain uniformly bounded as the discount factor approaches one.

cs.LG↗

arXiv2025

On the embedding transformation for optimal control of multi-mode switched systems

This paper develops an embedding-based approach to solve switched optimal control problems (SOCPs) with an arbitrary number of subsystems. Initially, the discrete switching signal is represented by a set of binary variables, encoding each mode in binary format. An embedded optimal control problem (EOCP) is then formulated by replacing these binary variables with continuous embedded variables that can take intermediate values between zero and one. Although embedding allows SOCPs to be addressed using conventional techniques, the optimal solutions of EOCPs often yield intermediate values for binary variables, which may not be feasible for the original SOCP. To address this challenge, a modified EOCP (MEOCP) is introduced by adding a concave auxiliary cost function of appropriate dimensionality to the main cost function. This addition ensures that the optimal solution of the EOCP is bang-bang, and as a result, feasible for the original SOCP.

eess.SY↗

arXiv2025

Switched Optimal Control with Dwell Time Constraints

This paper presents an embedding-based approach for solving switched optimal control problems (SOCPs) with dwell time constraints. At first, an embedded optimal control problem (EOCP) is defined by replacing the discrete switching signal with a continuous embedded variable that can take intermediate values between the discrete modes. While embedding enables solutions of SOCPs via conventional techniques, optimal solutions of EOCPs often involve nonexistent modes and thus may not be feasible for the SOCP. In the modified EOCP (MEOCP), a concave function is added to the cost function to enforce a bang-bang solution in the embedded variable, which results in feasible solutions for the SOCP. However, the MEOCP cannot guarantee the satisfaction of dwell-time constraints. In this paper, a MEOCP is combined with a filter layer to remove switching times that violate the dwell time constraint. Insertion gradients are used to minimize the effect of the filter on the optimal cost.

math.OC↗