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Dans cette thèse, on s'intéresse à l'étude d'existence de solutions pour les processus de rafle. Ce problème prend la forme d'une inclusion différentielle contrainte avec des cônes normaux qui apparaissent naturellement dans nombreuses applications telles que le mouvement de foule, l'élastoplasticité, les mécaniques, les circuits électroniques, etc. L'objective de ce travail est de rapprocher deux importantes classes d'inclusions différentielles. D'une part, nous établissons quelques résultats d'existence de tube-solutions pour des processus de rafle à des ensembles uniformément prox-réguliers. D'autre part, nous présentons des résultats d'existence de solutions monotone par rapport à un préordre pour un système mixte d'inclusions différentielles projetées. De plus, nous montrons l'existence d'un point-selle pour notre système et nous fournissons deux exemples d'applications. / In this thesis, we were interested in the study of the existence of solutions for sweeping processes. This problem takes the form of a constrained differential inclusion involving normal cones which appears naturally in many applications such as crowd motion, elastoplasticity, mechanics, electrical circuit, etc.The aim of this work is to bring together two classes of differential inclusions. On one hand, we establish some existence results of solutions-tube for sweeping processes with uniformly prox-regular sets. On the other hand, we present existence results of monotone solutions with respect to a preorder for a mixed system of projected differential inclusions. In addition, we show that our system has a saddle-point and we provide two examples of applications.

Advances in digital signal processing (DSP) and computing technology have resulted in the emergence of increasingly adaptive radar systems. It is clear that the Electronic Attack (EA), or jamming, of such radar systems is expected to become a more difficult task. The reason for this research was to address the issue of jamming adaptive radar systems. This required consideration of adaptive jamming systems and the development of a methodology for outlining the features of such a system is proposed as the key contribution of this thesis. For the first time, game-based optimization methods have been applied to a maritime counter-surveillance/counter-targeting scenario involving conventional, as well as so-called ‘smart’ noise jamming.Conventional noise jamming methods feature prominently in the origins of radar electronic warfare, and are still widely implemented. They have been well studied, and are important for comparisons with coherent jamming techniques.Moreover, noise jamming is more readily applied with limited information support and is therefore germane to the problem of jamming adaptive radars; during theearly stages when the jammer tries to learn about the radar’s parameters and its own optimal actions.A radar and a jammer were considered as informed opponents ‘playing’ in a non-cooperative two-player, zero-sum game. The effects of jamming on the target detection performance of a radar using Constant False Alarm Rate (CFAR)processing were analyzed using a game theoretic approach for three cases: (1) Ungated Range Noise (URN), (2) Range-Gated Noise (RGN) and (3) False-Target (FT) jamming.Assuming a Swerling type II target in the presence of Rayleigh-distributed clutter, utility functions were described for Cell-Averaging (CA) and Order Statistic (OS) CFAR processors and the three cases of jamming. The analyses included optimizations of these utility functions, subject to certain constraints, with respectto control variables (strategies) in the jammer, such as jammer power and spatial extent of jamming, and control variables in the radar, such as threshold parameter and reference window size. The utility functions were evaluated over the players’ strategy sets and the resulting matrix-form games were solved for the optimal or ‘best response’ strategies of both the jammer and the radar.

Advances in digital signal processing (DSP) and computing technology have resulted in the emergence of increasingly adaptive radar systems. It is clear that the Electronic Attack (EA), or jamming, of such radar systems is expected to become a more difficult task. The reason for this research was to address the issue of jamming adaptive radar systems. This required consideration of adaptive jamming systems and the development of a methodology for outlining the features of such a system is proposed as the key contribution of this thesis. For the first time, game-based optimization methods have been applied to a maritime counter-surveillance/counter-targeting scenario involving conventional, as well as so-called ‘smart’ noise jamming.Conventional noise jamming methods feature prominently in the origins of radar electronic warfare, and are still widely implemented. They have been well studied, and are important for comparisons with coherent jamming techniques.Moreover, noise jamming is more readily applied with limited information support and is therefore germane to the problem of jamming adaptive radars; during theearly stages when the jammer tries to learn about the radar’s parameters and its own optimal actions.A radar and a jammer were considered as informed opponents ‘playing’ in a non-cooperative two-player, zero-sum game. The effects of jamming on the target detection performance of a radar using Constant False Alarm Rate (CFAR)processing were analyzed using a game theoretic approach for three cases: (1) Ungated Range Noise (URN), (2) Range-Gated Noise (RGN) and (3) False-Target (FT) jamming.Assuming a Swerling type II target in the presence of Rayleigh-distributed clutter, utility functions were described for Cell-Averaging (CA) and Order Statistic (OS) CFAR processors and the three cases of jamming. The analyses included optimizations of these utility functions, subject to certain constraints, with respectto control variables (strategies) in the jammer, such as jammer power and spatial extent of jamming, and control variables in the radar, such as threshold parameter and reference window size. The utility functions were evaluated over the players’ strategy sets and the resulting matrix-form games were solved for the optimal or ‘best response’ strategies of both the jammer and the radar.