A probability-theoretic problem under information constraints for the concept of optimal control over a noisymemoryless channel is considered. For our Observer-Controller block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a Blahut-Arimoto-type algorithm − which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for min. This problem is an N P−hard and non-convex multi-objective optimisation (MOO) one, were the objective functions are respectively the distortion function dim Null I( Ŝ; S → ∞ and the memorylesschannel capacity dim Null I(X; X → 0. Our novel algorithm applies an Alternating optimisation method. Subsequently, a robust version of the algorithm is discussed with regard to the perturbed PMFs − parameter uncertainties in general.The aforementioned robustness is actualised by exploiting the simultaneous-perturbation-stochastic-approximation (SPSA). The principles of detectability-and-stabilisability as well as synchronisability are explored, in addition to providing the simulationsby which the efficiency of our work is shown. We also calculate the total complexity of our proposed algorithms respectively as O T K M 0 K log K and O T K M 0 K log K + 0.33K . Our methodology is generic which can be applied to other fields of studies which are optimisation-driven.