Adversarial attacks play a pivotal role in testing and improving the reliability of deep learning (DL) systems. Existing literature has demonstrated that subtle perturbations to the input can elicit erroneous outcomes, thereby substantially compromising the security of DL systems. This has emerged as a critical concern in the development of DL-based safety-critical systems like Autonomous Driving Systems (ADSs). The focus of existing adversarial attack methods on End-to-End (E2E) ADSs has predominantly centered on misbehaviors of steering angle, which overlooks speed-related controls or imperceptible perturbations. To address these challenges, we introduce UniAda, a multi-objective white-box attack technique with a core function that revolves around crafting an image-agnostic adversarial perturbation capable of simultaneously influencing both steering and speed controls. UniAda capitalizes on an intricately designed multi-objective optimization function with the Adaptive Weighting Scheme (AWS), enabling the concurrent optimization of diverse objectives. Validated with both simulated and real-world driving data, UniAda outperforms five benchmarks across two metrics, inducing steering and speed deviations from 3.54 degrees to 29 degrees and 11 km per hour to 22 km per hour on average. This systematic approach establishes UniAda as a proven technique for adversarial attacks on modern DL-based E2E ADSs.